Finite Group Databasebeta

← C41×#26809 #23803010

Subgroups — C41×#26809 #23803010

Order 10496.

776 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#485C211yesmaximal, characteristic
2C2×C41×#479C211yesmaximal, characteristic, complemented
3C41×#2489C211yesmaximal, characteristic
4C41×#2362C211yesmaximal, characteristic
5C41×#2068C211yesmaximal, characteristic, complemented
6C41×#2059C211yesmaximal, characteristic, complemented
7C41×#2036C211yesmaximal, characteristic
8C41×#2001C211yesmaximal, characteristic
9C41×#1971C211yesmaximal, characteristic, complemented
10C41×#1928C211yesmaximal, characteristic, complemented
11C41×#1928C211yesmaximal, characteristic, complemented
12C41×#1924C211yesmaximal, characteristic
13C41×#1878C211yesmaximal, characteristic, complemented
14C41×#1854C211yesmaximal, characteristic
15C41×#1776C211yesmaximal, characteristic, complemented
16C22×Q16×C41C2211yescharacteristic
17C2×#125×C41C2211yescharacteristic
18C2×C22⋊Q8×C41C2211yescharacteristic
19C2×C22⋊Q8×C41C2211yescharacteristic
20C2×C4×Q8×C41C2211yescharacteristic
21C2×#117×C41C2211yescharacteristic
22C41×#485—24no—
23C41×#479—24no—
24C2×#107×C41C2211yescharacteristic
25C2×#107×C41C2211yescharacteristic
26C2×#107×C41C2211yescharacteristic
27C2×#106×C41C2211yescharacteristic
28C2×#106×C41C2211yescharacteristic
29C2×C4⋊C8×C41C2211yescharacteristic
30C2×#103×C41C2211yescharacteristic
31C2×#103×C41C2211yescharacteristic
32C2×#103×C41C2211yescharacteristic
33C2×#103×C41C2211yescharacteristic
34C2×#103×C41C2211yescharacteristic
35C2×#103×C41C2211yescharacteristic
36C2×C22⋊C8×C41C2211yescharacteristic
37C2×C22⋊C8×C41C2211yescharacteristic
38C2×#97×C41C2211yescharacteristic
39C41×#400—21no—
40C41×#397—21no—
41C41×#391C2211yescharacteristic
42C41×#391C2211yescharacteristic
43C41×#391C2211yescharacteristic
44C41×#389C2211yescharacteristic
45C41×#388—21no—
46C41×#388—21no—
47C41×#388—21no—
48C41×#387—21no—
49C41×#382—21no—
50C41×#380C2211yescharacteristic
51C4×C4⋊C4×C41—21no—
52C4×C4⋊C4×C41C2211yescharacteristic
53C4×C4⋊C4×C41C2211yescharacteristic
54C4×C22⋊C4×C41C2211yescharacteristic
55C41×#340C2211yescharacteristic
56C41×#340C2211yescharacteristic
57C41×#340C2211yescharacteristic
58C41×#340C2211yescharacteristic
59C41×#336C2211yescharacteristic
60C41×#336C2211yescharacteristic
61C22×Q8×C41C2311yescharacteristic
62C22×Q8×C41C2311yescharacteristic
63C23×C4×C41C2311yescharacteristic
64C2×Q16×C41—22no—
65C2×Q16×C41—22no—
66C2×Q16×C41—41no—
67C22×C8×C41C2311yescharacteristic
68C22×C8×C41C2311yescharacteristic
69C22×C8×C41C2311yescharacteristic
70C22×C8×C41C2311yescharacteristic
71#125×C41—22no—
72#125×C41—41no—
73C22⋊Q8×C41—22no—
74C22⋊Q8×C41—22no—
75C22⋊Q8×C41—22no—
76C22⋊Q8×C41—41no—
77C4×Q8×C41—22no—
78C4×Q8×C41—41no—
79#117×C41—22no—
80#117×C41—41no—
81C2×C4⋊C4×C41—21no—
82C2×C4⋊C4×C41—21no—
83C2×C4⋊C4×C41—21no—
84C2×C4⋊C4×C41—21no—
85C2×C4⋊C4×C41—21no—
86C2×C4⋊C4×C41—21no—
87C2×C4⋊C4×C41C2311yescharacteristic
88C2×C4⋊C4×C41C2311yescharacteristic
89C2×C4⋊C4×C41C2311yescharacteristic
90C2×C4⋊C4×C41C2311yescharacteristic
91C2×C4⋊C4×C41C2311yescharacteristic
92C2×C4⋊C4×C41C2311yescharacteristic
93C2×C22⋊C4×C41—21no—
94C2×C22⋊C4×C41—21no—
95C2×C22⋊C4×C41—21no—
96C2×C22⋊C4×C41—21no—
97C2×C22⋊C4×C41D411yescharacteristic
98C2×C22⋊C4×C41D411yescharacteristic
99C2×C42×C41—21no—
100C2×C42×C41—21no—
101C2×C42×C41—21no—
102C2×C42×C41—21no—
103C2×C42×C41C2311yescharacteristic
104C2×C42×C41C2311yescharacteristic
105#107×C41—22no—
106#107×C41—22no—
107#107×C41—22no—
108#106×C41—41no—
109#106×C41D414yes—
110C4⋊C8×C41—22no—
111#103×C41—22no—
112#103×C41—22no—
113#103×C41—22no—
114#103×C41—22no—
115#103×C41—22no—
116#103×C41—22no—
117C22⋊C8×C41—22no—
118C22⋊C8×C41—22no—
119#97×C41—22no—
120#95×C41—21no—
121#95×C41—21no—
122#95×C41—21no—
123#95×C41—21no—
124#95×C41—21no—
125#95×C41—21no—
126#95×C41—21no—
127#95×C41—21no—
128#95×C41—21no—
129#95×C41—21no—
130#95×C41D411yescharacteristic
131#95×C41D411yescharacteristic
132C24×C41C2×D411yescharacteristic
133C2×Q8×C41—21no—
134C2×Q8×C41—21no—
135C2×Q8×C41—21no—
136C2×Q8×C41—21no—
137C2×Q8×C41—21no—
138C2×Q8×C41—21no—
139C2×Q8×C41—21no—
140C2×Q8×C41—21no—
141C2×Q8×C41—21no—
142C2×Q8×C41—21no—
143C2×Q8×C41—21no—
144C2×Q8×C41#4112yes—
145C22×C4×C41—21no—
146C22×C4×C41—21no—
147C22×C4×C41—21no—
148C22×C4×C41—21no—
149C22×C4×C41—21no—
150C22×C4×C41—21no—
151C22×C4×C41—21no—
152C22×C4×C41—21no—
153C22×C4×C41—21no—
154C22×C4×C41—21no—
155C22×C4×C41—21no—
156C22×C4×C41—21no—
157C22×C4×C41—21no—
158C22×C4×C41—21no—
159C22×C4×C41C2×D411yescharacteristic
160C22×C4×C41C2×D411yescharacteristic
161C22×C4×C41C2×D411yescharacteristic
162C22×C4×C41C2×D411yescharacteristic
163C22×C4×C41C2×D411yescharacteristic
164C22×C4×C41C2411yescharacteristic
165Q16×C41—44no—
166C2×C8×C41—21no—
167C2×C8×C41—21no—
168C2×C8×C41—21no—
169C2×C8×C41—21no—
170C2×C8×C41—21no—
171C2×C8×C41—21no—
172C2×C8×C41—21no—
173C2×C8×C41—21no—
174C2×C8×C41—21no—
175C2×C8×C41—21no—
176C2×C8×C41C2×D412yes—
177C2×C8×C41#4112yes—
178C4⋊C4×C41—24no—
179C4⋊C4×C41—21no—
180C4⋊C4×C41—21no—
181C4⋊C4×C41—21no—
182C4⋊C4×C41—21no—
183C4⋊C4×C41—21no—
184C4⋊C4×C41—21no—
185C4⋊C4×C41—21no—
186C4⋊C4×C41—21no—
187C4⋊C4×C41—21no—
188C4⋊C4×C41—42no—
189C4⋊C4×C41—42no—
190C4⋊C4×C41—42no—
191C4⋊C4×C41—42no—
192C4⋊C4×C41—42no—
193C4⋊C4×C41C2×D412yes—
194C4⋊C4×C41C2×D412yes—
195C4⋊C4×C41#4112yes—
196C22⋊C4×C41—24no—
197C22⋊C4×C41—41no—
198C22⋊C4×C41—41no—
199C22⋊C4×C41—42no—
200C22⋊C4×C41—42no—
201C22⋊C4×C41—42no—
202C42×C41—21no—
203C42×C41—21no—
204C42×C41—21no—
205C42×C41—21no—
206C42×C41—42no—
207C42×C41—42no—
208C42×C41—42no—
209C42×C41—42no—
210C23×C41—21no—
211C23×C41—21no—
212C23×C41—21no—
213C23×C41—21no—
214C23×C41—21no—
215C23×C41—21no—
216C23×C41—21no—
217C23×C41C22×D411yescharacteristic
218Q8×C41—22no—
219Q8×C41—22no—
220Q8×C41—41no—
221Q8×C41—41no—
222Q8×C41—41no—
223Q8×C41—41no—
224Q8×C41—41no—
225Q8×C41—41no—
226C2×C4×C41—22no—
227C2×C4×C41—22no—
228C2×C4×C41—21no—
229C2×C4×C41—21no—
230C2×C4×C41—21no—
231C2×C4×C41—22no—
232C2×C4×C41—21no—
233C2×C4×C41—22no—
234C2×C4×C41—21no—
235C2×C4×C41—21no—
236C2×C4×C41—21no—
237C2×C4×C41—21no—
238C2×C4×C41—21no—
239C2×C4×C41—21no—
240C2×C4×C41—21no—
241C2×C4×C41—21no—
242C2×C4×C41—21no—
243C2×C4×C41—21no—
244C2×C4×C41—21no—
245C2×C4×C41—41no—
246C2×C4×C41—41no—
247C2×C4×C41—41no—
248C2×C4×C41—41no—
249C2×C4×C41—41no—
250C2×C4×C41—41no—
251C2×C4×C41—41no—
252C2×C4×C41—41no—
253C2×C4×C41—41no—
254C2×C4×C41—41no—
255C2×C4×C41—41no—
256C2×C4×C41—41no—
257C2×C4×C41—41no—
258C2×C4×C41—41no—
259C2×C4×C41—41no—
260C2×C4×C41—41no—
261C2×C4×C41—41no—
262C2×C4×C41—41no—
263C2×C4×C41—41no—
264C2×C4×C41—41no—
265C2×C4×C41—41no—
266C2×C4×C41—41no—
267C2×C4×C41—41no—
268C2×C4×C41—41no—
269C2×C4×C41C22×D411yescharacteristic
270C2×C4×C41C2×#4111yescharacteristic
271C2×C4×C41C2×#4111yescharacteristic
272C2×C4×C41C2×#4111yescharacteristic
273C2×C4×C41H(5,𝔽2)11yescharacteristic
274C2×C4×C412−1+411yescharacteristic
275C8×C41—22no—
276C8×C41—22no—
277C8×C41—41no—
278C8×C41—41no—
279#26809C4111yesmaximal, characteristic, direct product factor, Sylow
280C22×C41—41no—
281C22×C41—41no—
282C22×C41—41no—
283C22×C41—41no—
284C22×C41—41no—
285C22×C41—41no—
286C22×C41—41no—
287C22×C41#52511yescharacteristic
288C22×C41D4211yescharacteristic
289C22×C41#54711yescharacteristic
290C22×C41#57511yescharacteristic
291C22×C41#57511yescharacteristic
292C22×C41#57811yescharacteristic
293C22×C41#57811yescharacteristic
294C4×C41—41no—
295C4×C41—41no—
296C4×C41—42no—
297C4×C41—41no—
298C4×C41—42no—
299C4×C41—41no—
300C4×C41—41no—
301C4×C41—42no—
302C4×C41—42no—
303C4×C41—81no—
304C4×C41—81no—
305C4×C41—81no—
306C4×C41—81no—
307C4×C41#53211yescharacteristic
308C4×C41#54211yescharacteristic
309C4×C41#54811yescharacteristic
310C4×C41#55111yescharacteristic
311C2×#485C2×C4111yescharacteristic
312C2×#479C2×C4111yescharacteristic, complemented
313#2489C2×C4111yescharacteristic
314#2362C2×C4111yescharacteristic
315#2068C2×C4111yescharacteristic, complemented
316#2059C2×C4111yescharacteristic, complemented
317#2036C2×C4111yescharacteristic
318#2001C2×C4111yescharacteristic
319#1971C2×C4111yescharacteristic, complemented
320#1928C2×C4111yescharacteristic, complemented
321#1928C2×C4111yescharacteristic, complemented
322#1924C2×C4111yescharacteristic
323#1878C2×C4111yescharacteristic, complemented
324#1854C2×C4111yescharacteristic
325#1776C2×C4111yescharacteristic, complemented
326C2×C41—81no—
327C2×C41#246111yescharacteristic
328C2×C41#311111yescharacteristic
329C2×C41#312711yescharacteristic
330C2×C41#326911yescharacteristic
331C2×C41#326911yescharacteristic
332C2×C41#334911yescharacteristic
333C2×C41#335211yescharacteristic
334C22×Q16C22×C4111yescharacteristic
335C2×#125C22×C4111yescharacteristic
336C2×C22⋊Q8C22×C4111yescharacteristic
337C2×C22⋊Q8C22×C4111yescharacteristic
338C2×C4×Q8C22×C4111yescharacteristic
339C2×#117C22×C4111yescharacteristic
340#485—24no—
341#479—24no—
342C2×#107C22×C4111yescharacteristic
343C2×#107C22×C4111yescharacteristic
344C2×#107C22×C4111yescharacteristic
345C2×#106C22×C4111yescharacteristic
346C2×#106C22×C4111yescharacteristic
347C2×C4⋊C8C22×C4111yescharacteristic
348C2×#103C22×C4111yescharacteristic
349C2×#103C22×C4111yescharacteristic
350C2×#103C22×C4111yescharacteristic
351C2×#103C22×C4111yescharacteristic
352C2×#103C22×C4111yescharacteristic
353C2×#103C22×C4111yescharacteristic
354C2×C22⋊C8C22×C4111yescharacteristic
355C2×C22⋊C8C22×C4111yescharacteristic
356C2×#97C22×C4111yescharacteristic
357#400—21no—
358#397—21no—
359#391C22×C4111yescharacteristic
360#391C22×C4111yescharacteristic
361#391C22×C4111yescharacteristic
362#389C22×C4111yescharacteristic
363#388—21no—
364#388—21no—
365#388—21no—
366#387—21no—
367#382—21no—
368#380C22×C4111yescharacteristic
369C4×C4⋊C4—21no—
370C4×C4⋊C4C22×C4111yescharacteristic
371C4×C4⋊C4C22×C4111yescharacteristic
372C4×C22⋊C4C22×C4111yescharacteristic
373#340C22×C4111yescharacteristic
374#340C22×C4111yescharacteristic
375#340C22×C4111yescharacteristic
376#340C22×C4111yescharacteristic
377#336C22×C4111yescharacteristic
378#336C22×C4111yescharacteristic
379C41#2680911yescharacteristic, direct product factor, Sylow
380C22×Q8C23×C4111yescharacteristic
381C22×Q8C23×C4111yescharacteristic
382C23×C4C23×C4111yescharacteristic
383C2×Q16—22no—
384C2×Q16—22no—
385C2×Q16—41no—
386C22×C8C23×C4111yescharacteristic
387C22×C8C23×C4111yescharacteristic
388C22×C8C23×C4111yescharacteristic
389C22×C8C23×C4111yescharacteristic
390#125—22no—
391#125—41no—
392C22⋊Q8—22no—
393C22⋊Q8—22no—
394C22⋊Q8—22no—
395C22⋊Q8—41no—
396C4×Q8—22no—
397C4×Q8—41no—
398#117—22no—
399#117—41no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4C23×C4111yescharacteristic
407C2×C4⋊C4C23×C4111yescharacteristic
408C2×C4⋊C4C23×C4111yescharacteristic
409C2×C4⋊C4C23×C4111yescharacteristic
410C2×C4⋊C4C23×C4111yescharacteristic
411C2×C4⋊C4C23×C4111yescharacteristic
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4D4×C4111yescharacteristic
417C2×C22⋊C4D4×C4111yescharacteristic
418C2×C42—21no—
419C2×C42—21no—
420C2×C42—21no—
421C2×C42—21no—
422C2×C42C23×C4111yescharacteristic
423C2×C42C23×C4111yescharacteristic
424#107—22no—
425#107—22no—
426#107—22no—
427#106—41no—
428#106D4×C4114yes—
429C4⋊C8—22no—
430#103—22no—
431#103—22no—
432#103—22no—
433#103—22no—
434#103—22no—
435#103—22no—
436C22⋊C8—22no—
437C22⋊C8—22no—
438#97—22no—
439#95—21no—
440#95—21no—
441#95—21no—
442#95—21no—
443#95—21no—
444#95—21no—
445#95—21no—
446#95—21no—
447#95—21no—
448#95—21no—
449#95D4×C4111yescharacteristic
450#95D4×C4111yescharacteristic
451C24C2×D4×C4111yescharacteristic
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8#41×C4112yes—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4C2×D4×C4111yescharacteristic
479C22×C4C2×D4×C4111yescharacteristic
480C22×C4C2×D4×C4111yescharacteristic
481C22×C4C2×D4×C4111yescharacteristic
482C22×C4C2×D4×C4111yescharacteristic
483C22×C4C24×C4111yescharacteristic
484Q16—44no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8C2×D4×C4112yes—
496C2×C8#41×C4112yes—
497C4⋊C4—24no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—42no—
508C4⋊C4—42no—
509C4⋊C4—42no—
510C4⋊C4—42no—
511C4⋊C4—42no—
512C4⋊C4C2×D4×C4112yes—
513C4⋊C4C2×D4×C4112yes—
514C4⋊C4#41×C4112yes—
515C22⋊C4—24no—
516C22⋊C4—41no—
517C22⋊C4—41no—
518C22⋊C4—42no—
519C22⋊C4—42no—
520C22⋊C4—42no—
521C42—21no—
522C42—21no—
523C42—21no—
524C42—21no—
525C42—42no—
526C42—42no—
527C42—42no—
528C42—42no—
529C23—21no—
530C23—21no—
531C23—21no—
532C23—21no—
533C23—21no—
534C23—21no—
535C23—21no—
536C23C22×D4×C4111yescharacteristic
537Q8—22no—
538Q8—22no—
539Q8—41no—
540Q8—41no—
541Q8—41no—
542Q8—41no—
543Q8—41no—
544Q8—41no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—22no—
551C2×C4—21no—
552C2×C4—22no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4C22×D4×C4111yescharacteristic
589C2×C4C2×#41×C4111yescharacteristic
590C2×C4C2×#41×C4111yescharacteristic
591C2×C4C2×#41×C4111yescharacteristic
592C2×C4H(5,𝔽2)×C4111yescharacteristic
593C2×C42−1+4×C4111yescharacteristic
594C8—22no—
595C8—22no—
596C8—41no—
597C8—41no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22C41×#52511yescharacteristic
606C22D42×C4111yescharacteristic
607C22C41×#54711yescharacteristic
608C22C41×#57511yescharacteristic
609C22C41×#57511yescharacteristic
610C22C41×#57811yescharacteristic
611C22C41×#57811yescharacteristic
612C4—41no—
613C4—41no—
614C4—42no—
615C4—41no—
616C4—42no—
617C4—41no—
618C4—41no—
619C4—42no—
620C4—42no—
621C4—81no—
622C4—81no—
623C4—81no—
624C4—81no—
625C4C41×#53211yescharacteristic
626C4C41×#54211yescharacteristic
627C4C41×#54811yescharacteristic
628C4C41×#55111yescharacteristic
629C2—81no—
630C2C41×#246111yescharacteristic
631C2C41×#311111yescharacteristic
632C2C41×#312711yescharacteristic
633C2C41×#326911yescharacteristic
634C2C41×#326911yescharacteristic
635C2C41×#334911yescharacteristic
636C2C41×#335211yescharacteristic
subgroupG/H
center, socleC23×C41C22×D4
commutator, Frattini, cosocleC22×C4C24×C41
prime radicalC24×C41C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C41 ◁ C4×C22⋊C4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C41×#479C2semidirect
5. C41×#2068C2semidirect
6. C41×#2059C2semidirect
9. C41×#1971C2semidirect
10. C41×#1928C2semidirect
11. C41×#1928C2semidirect
13. C41×#1878C2semidirect
15. C41×#1776C2semidirect
279. #26809C41direct (N × H)
312. C2×#479C2×C41semidirect
315. #2068C2×C41semidirect
316. #2059C2×C41semidirect
319. #1971C2×C41semidirect
320. #1928C2×C41semidirect
321. #1928C2×C41semidirect
323. #1878C2×C41semidirect
325. #1776C2×C41semidirect
379. C41#26809direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C41×#4852
C2×C41×#4792
C41×#24892
C41×#23622
C41×#20682
C41×#20592
C41×#20362
C41×#20012
C41×#19712
C41×#19282
C41×#19242
C41×#18782
C41×#18542
C41×#17762
#2680941