Finite Group Databasebeta

← C2×C41×#1618 #23794321

Subgroups — C2×C41×#1618 #23794321

Order 10496.

1200 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#538C211yesmaximal, characteristic
2C2×C41×#484C211yesmaximal, characteristic, complemented
3C2×C41×#481C211yesmaximal, characteristic, complemented
4C2×C41×#399C211yesmaximal, characteristic, complemented
5C41×#1618C218yesmaximal, direct product factor
6C2×C41×#328C211yesmaximal, characteristic, complemented
7C2×C41×#327C211yesmaximal, characteristic, complemented
8C2×C41×#323C211yesmaximal, characteristic, complemented
9C41×#538—22no—
10C41×#538—22no—
11C41×#538—22no—
12C41×#538C2214yes—
13C2×#126×C41—21no—
14C2×#124×C41—21no—
15C2×#123×C41—21no—
16C2×C22⋊Q8×C41C2211yescharacteristic
17C2×#121×C41—21no—
18C2×#121×C41C2211yescharacteristic
19C2×#120×C41—21no—
20C2×C4×D4×C41—21no—
21C22×C4⋊C4×C41—21no—
22C22×C4⋊C4×C41C2211yescharacteristic
23C22×C22⋊C4×C41—21no—
24C22×C22⋊C4×C41C2211yescharacteristic
25C41×#484—22no—
26C41×#484C2214yescomplemented
27C41×#481—22no—
28C41×#481C2214yescomplemented
29C2×#107×C41—21no—
30C2×#106×C41—21no—
31C2×#103×C41—21no—
32C2×#102×C41—21no—
33C2×C22⋊C8×C41C2211yescharacteristic
34C2×C22⋊C8×C41C2211yescharacteristic
35C41×#399—22no—
36C41×#399C2214yescomplemented
37C2×#95×C41C2211yescharacteristic
38C41×#328C2214yescomplemented
39C41×#327C2214yescomplemented
40C41×#323C2214yescomplemented
41C25×C41D411yescharacteristic
42C22×Q8×C41D411yescharacteristic
43C22×D4×C41—21no—
44C22×D4×C41—21no—
45C22×D4×C41—21no—
46C22×D4×C41D411yescharacteristic
47C23×C4×C41—21no—
48C23×C4×C41—21no—
49C23×C4×C41—21no—
50C23×C4×C41D411yescharacteristic
51C23×C4×C41C2311yescharacteristic
52C22×C8×C41—21no—
53C22×C8×C41—21no—
54#126×C41—24no—
55#126×C41—24no—
56#124×C41—24no—
57#124×C41—24no—
58#123×C41—24no—
59#123×C41—24no—
60C22⋊Q8×C41—21no—
61C22⋊Q8×C41—21no—
62C22⋊Q8×C41D412yes—
63C22⋊Q8×C41C2312yes—
64#121×C41—24no—
65#121×C41—24no—
66#121×C41—21no—
67#121×C41—21no—
68#121×C41D412yes—
69#121×C41C2312yes—
70#120×C41—24no—
71#120×C41—24no—
72C4×D4×C41—24no—
73C4×D4×C41—24no—
74C2×C4⋊C4×C41—21no—
75C2×C4⋊C4×C41—21no—
76C2×C4⋊C4×C41—21no—
77C2×C4⋊C4×C41—21no—
78C2×C4⋊C4×C41—21no—
79C2×C4⋊C4×C41—21no—
80C2×C4⋊C4×C41—24no—
81C2×C4⋊C4×C41—21no—
82C2×C4⋊C4×C41—44no—
83C2×C4⋊C4×C41D411yescharacteristic
84C2×C4⋊C4×C41D411yescharacteristic
85C2×C4⋊C4×C41C2312yes—
86C2×C22⋊C4×C41—21no—
87C2×C22⋊C4×C41—21no—
88C2×C22⋊C4×C41—21no—
89C2×C22⋊C4×C41—21no—
90C2×C22⋊C4×C41—21no—
91C2×C22⋊C4×C41—21no—
92C2×C22⋊C4×C41—21no—
93C2×C22⋊C4×C41—21no—
94C2×C22⋊C4×C41—21no—
95C2×C22⋊C4×C41—24no—
96C2×C22⋊C4×C41—44no—
97C2×C22⋊C4×C41D412yes—
98C2×C22⋊C4×C41C2312yes—
99C2×C42×C41—21no—
100#107×C41—24no—
101#106×C41—24no—
102#103×C41—24no—
103#102×C41—24no—
104C22⋊C8×C41—21no—
105C22⋊C8×C41—21no—
106C22⋊C8×C41C2312yes—
107C22⋊C8×C41C2312yes—
108#95×C41—21no—
109#95×C41C2312yes—
110C24×C41—21no—
111C24×C41—21no—
112C24×C41—22no—
113C24×C41—21no—
114C24×C41—22no—
115C24×C41—42no—
116C24×C41—42no—
117C24×C41C2×D411yescharacteristic
118C24×C41C2×D412yes—
119C2×Q8×C41—21no—
120C2×Q8×C41—42no—
121C2×Q8×C41C2×D412yes—
122C2×D4×C41—22no—
123C2×D4×C41—22no—
124C2×D4×C41—24no—
125C2×D4×C41—24no—
126C2×D4×C41—21no—
127C2×D4×C41—42no—
128C2×D4×C41—42no—
129C2×D4×C41—42no—
130C2×D4×C41—82no—
131C2×D4×C41—82no—
132C2×D4×C41C2×D412yes—
133C22×C4×C41—24no—
134C22×C4×C41—21no—
135C22×C4×C41—21no—
136C22×C4×C41—21no—
137C22×C4×C41—21no—
138C22×C4×C41—22no—
139C22×C4×C41—24no—
140C22×C4×C41—21no—
141C22×C4×C41—22no—
142C22×C4×C41—42no—
143C22×C4×C41—42no—
144C22×C4×C41—42no—
145C22×C4×C41—42no—
146C22×C4×C41—42no—
147C22×C4×C41—42no—
148C22×C4×C41—41no—
149C22×C4×C41—41no—
150C22×C4×C41—82no—
151C22×C4×C41C2×D411yescharacteristic
152C22×C4×C41C2×D411yescharacteristic
153C22×C4×C41C2×D412yes—
154C22×C4×C41C2×D411yescharacteristic
155C22×C4×C41C2×D411yescharacteristic
156C22×C4×C41C2×D411yescharacteristic
157C22×C4×C41C2411yescharacteristic
158C2×C8×C41—22no—
159C2×C8×C41—22no—
160C2×C8×C41—42no—
161C2×C8×C41—42no—
162C4⋊C4×C41—24no—
163C4⋊C4×C41—22no—
164C4⋊C4×C41—21no—
165C4⋊C4×C41—21no—
166C4⋊C4×C41—22no—
167C4⋊C4×C41—22no—
168C4⋊C4×C41—22no—
169C4⋊C4×C41—48no—
170C4⋊C4×C41—41no—
171C4⋊C4×C41—41no—
172C4⋊C4×C41C2×D412yes—
173C4⋊C4×C41C2×D412yes—
174C22⋊C4×C41—24no—
175C22⋊C4×C41—24no—
176C22⋊C4×C41—24no—
177C22⋊C4×C41—22no—
178C22⋊C4×C41—22no—
179C22⋊C4×C41—22no—
180C22⋊C4×C41—22no—
181C22⋊C4×C41—22no—
182C22⋊C4×C41—22no—
183C22⋊C4×C41—22no—
184C22⋊C4×C41—22no—
185C22⋊C4×C41—48no—
186C42×C41—24no—
187C23×C41—22no—
188C23×C41—22no—
189C23×C41—22no—
190C23×C41—22no—
191C23×C41—22no—
192C23×C41—22no—
193C23×C41—42no—
194C23×C41—42no—
195C23×C41—48no—
196C23×C41—42no—
197C23×C41—42no—
198C23×C41—42no—
199C23×C41—42no—
200C23×C41—42no—
201C23×C41—42no—
202C23×C41—42no—
203C23×C41—81no—
204C23×C41—81no—
205C23×C41—84no—
206C23×C41#12011yescharacteristic
207C23×C41#12011yescharacteristic
208C23×C41#13512yes—
209C23×C41#13712yes—
210C23×C41C22×D411yescharacteristic
211Q8×C41—42no—
212Q8×C41—81no—
213D4×C41—42no—
214D4×C41—42no—
215D4×C41—42no—
216D4×C41—44no—
217D4×C41—81no—
218D4×C41—84no—
219D4×C41—84no—
220C2×C4×C41—22no—
221C2×C4×C41—22no—
222C2×C4×C41—24no—
223C2×C4×C41—22no—
224C2×C4×C41—22no—
225C2×C4×C41—22no—
226C2×C4×C41—22no—
227C2×C4×C41—41no—
228C2×C4×C41—41no—
229C2×C4×C41—41no—
230C2×C4×C41—41no—
231C2×C4×C41—48no—
232C2×C4×C41—42no—
233C2×C4×C41—42no—
234C2×C4×C41—42no—
235C2×C4×C41—42no—
236C2×C4×C41—42no—
237C2×C4×C41—42no—
238C2×C4×C41—42no—
239C2×C4×C41—42no—
240C2×C4×C41—42no—
241C2×C4×C41—42no—
242C2×C4×C41—81no—
243C2×C4×C41—84no—
244C2×C4×C41—82no—
245C2×C4×C41—82no—
246C2×C4×C41#12011yescharacteristic
247C2×C4×C41#12011yescharacteristic
248C2×C4×C41C22×D411yescharacteristic
249C2×C4×C41C22×D411yescharacteristic
250C8×C41—42no—
251C8×C41—42no—
252C2×#1618C4111yesmaximal, characteristic, direct product factor, Sylow
253C22×C41—24no—
254C22×C41—24no—
255C22×C41—21no—
256C22×C41—21no—
257C22×C41—21no—
258C22×C41—21no—
259C22×C41—44no—
260C22×C41—42no—
261C22×C41—42no—
262C22×C41—42no—
263C22×C41—42no—
264C22×C41—42no—
265C22×C41—42no—
266C22×C41—82no—
267C22×C41—84no—
268C22×C41—84no—
269C22×C41—84no—
270C22×C41#45212yes—
271C22×C41#45212yes—
272C22×C41#45312yes—
273C22×C41#45812yes—
274C22×C41C2×#12011yescharacteristic
275C22×C41C2×#13511yescharacteristic
276C22×C41C2×#13711yescharacteristic
277C4×C41—21no—
278C4×C41—21no—
279C4×C41—21no—
280C4×C41—21no—
281C4×C41—44no—
282C4×C41—42no—
283C4×C41—42no—
284C4×C41—42no—
285C4×C41—42no—
286C4×C41—82no—
287C2×#538C2×C4111yescharacteristic
288C2×#484C2×C4111yescharacteristic, complemented
289C2×#481C2×C4111yescharacteristic, complemented
290C2×#399C2×C4111yescharacteristic, complemented
291#1618C2×C4118yesdirect product factor
292C2×#328C2×C4111yescharacteristic, complemented
293C2×#327C2×C4111yescharacteristic, complemented
294C2×#323C2×C4111yescharacteristic, complemented
295C2×C41—21no—
296C2×C41—21no—
297C2×C41—22no—
298C2×C41—82no—
299C2×C41—82no—
300C2×C41#161814yesdirect product factor
301C2×C41C2×#45211yescharacteristic
302C2×C41C2×#45311yescharacteristic
303C2×C41C2×#45811yescharacteristic
304#538—22no—
305#538—22no—
306#538—22no—
307#538C22×C4114yes—
308C2×#126—21no—
309C2×#124—21no—
310C2×#123—21no—
311C2×C22⋊Q8C22×C4111yescharacteristic
312C2×#121—21no—
313C2×#121C22×C4111yescharacteristic
314C2×#120—21no—
315C2×C4×D4—21no—
316C22×C4⋊C4—21no—
317C22×C4⋊C4C22×C4111yescharacteristic
318C22×C22⋊C4—21no—
319C22×C22⋊C4C22×C4111yescharacteristic
320#484—22no—
321#484C22×C4114yescomplemented
322#481—22no—
323#481C22×C4114yescomplemented
324C2×#107—21no—
325C2×#106—21no—
326C2×#103—21no—
327C2×#102—21no—
328C2×C22⋊C8C22×C4111yescharacteristic
329C2×C22⋊C8C22×C4111yescharacteristic
330#399—22no—
331#399C22×C4114yescomplemented
332C2×#95C22×C4111yescharacteristic
333#328C22×C4114yescomplemented
334#327C22×C4114yescomplemented
335#323C22×C4114yescomplemented
336C41C2×#161811yescharacteristic, direct product factor, Sylow
337C25D4×C4111yescharacteristic
338C22×Q8D4×C4111yescharacteristic
339C22×D4—21no—
340C22×D4—21no—
341C22×D4—21no—
342C22×D4D4×C4111yescharacteristic
343C23×C4—21no—
344C23×C4—21no—
345C23×C4—21no—
346C23×C4D4×C4111yescharacteristic
347C23×C4C23×C4111yescharacteristic
348C22×C8—21no—
349C22×C8—21no—
350#126—24no—
351#126—24no—
352#124—24no—
353#124—24no—
354#123—24no—
355#123—24no—
356C22⋊Q8—21no—
357C22⋊Q8—21no—
358C22⋊Q8D4×C4112yes—
359C22⋊Q8C23×C4112yes—
360#121—24no—
361#121—24no—
362#121—21no—
363#121—21no—
364#121D4×C4112yes—
365#121C23×C4112yes—
366#120—24no—
367#120—24no—
368C4×D4—24no—
369C4×D4—24no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—24no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—44no—
379C2×C4⋊C4D4×C4111yescharacteristic
380C2×C4⋊C4D4×C4111yescharacteristic
381C2×C4⋊C4C23×C4112yes—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—44no—
393C2×C22⋊C4D4×C4112yes—
394C2×C22⋊C4C23×C4112yes—
395C2×C42—21no—
396#107—24no—
397#106—24no—
398#103—24no—
399#102—24no—
400C22⋊C8—21no—
401C22⋊C8—21no—
402C22⋊C8C23×C4112yes—
403C22⋊C8C23×C4112yes—
404#95—21no—
405#95C23×C4112yes—
406C24—21no—
407C24—21no—
408C24—22no—
409C24—21no—
410C24—22no—
411C24—42no—
412C24—42no—
413C24C2×D4×C4111yescharacteristic
414C24C2×D4×C4112yes—
415C2×Q8—21no—
416C2×Q8—42no—
417C2×Q8C2×D4×C4112yes—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—24no—
421C2×D4—24no—
422C2×D4—21no—
423C2×D4—42no—
424C2×D4—42no—
425C2×D4—42no—
426C2×D4—82no—
427C2×D4—82no—
428C2×D4C2×D4×C4112yes—
429C22×C4—24no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—24no—
436C22×C4—21no—
437C22×C4—22no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—82no—
447C22×C4C2×D4×C4111yescharacteristic
448C22×C4C2×D4×C4111yescharacteristic
449C22×C4C2×D4×C4112yes—
450C22×C4C2×D4×C4111yescharacteristic
451C22×C4C2×D4×C4111yescharacteristic
452C22×C4C2×D4×C4111yescharacteristic
453C22×C4C24×C4111yescharacteristic
454C2×C8—22no—
455C2×C8—22no—
456C2×C8—42no—
457C2×C8—42no—
458C4⋊C4—24no—
459C4⋊C4—22no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4—22no—
465C4⋊C4—48no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4C2×D4×C4112yes—
469C4⋊C4C2×D4×C4112yes—
470C22⋊C4—24no—
471C22⋊C4—24no—
472C22⋊C4—24no—
473C22⋊C4—22no—
474C22⋊C4—22no—
475C22⋊C4—22no—
476C22⋊C4—22no—
477C22⋊C4—22no—
478C22⋊C4—22no—
479C22⋊C4—22no—
480C22⋊C4—22no—
481C22⋊C4—48no—
482C42—24no—
483C23—22no—
484C23—22no—
485C23—22no—
486C23—22no—
487C23—22no—
488C23—22no—
489C23—42no—
490C23—42no—
491C23—48no—
492C23—42no—
493C23—42no—
494C23—42no—
495C23—42no—
496C23—42no—
497C23—42no—
498C23—42no—
499C23—81no—
500C23—81no—
501C23—84no—
502C23#120×C4111yescharacteristic
503C23#120×C4111yescharacteristic
504C23#135×C4112yes—
505C23#137×C4112yes—
506C23C22×D4×C4111yescharacteristic
507Q8—42no—
508Q8—81no—
509D4—42no—
510D4—42no—
511D4—42no—
512D4—44no—
513D4—81no—
514D4—84no—
515D4—84no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—24no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—48no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—81no—
539C2×C4—84no—
540C2×C4—82no—
541C2×C4—82no—
542C2×C4#120×C4111yescharacteristic
543C2×C4#120×C4111yescharacteristic
544C2×C4C22×D4×C4111yescharacteristic
545C2×C4C22×D4×C4111yescharacteristic
546C8—42no—
547C8—42no—
548C22—24no—
549C22—24no—
550C22—21no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—44no—
555C22—42no—
556C22—42no—
557C22—42no—
558C22—42no—
559C22—42no—
560C22—42no—
561C22—82no—
562C22—84no—
563C22—84no—
564C22—84no—
565C22C41×#45212yes—
566C22C41×#45212yes—
567C22C41×#45312yes—
568C22C41×#45812yes—
569C22C2×#120×C4111yescharacteristic
570C22C2×#135×C4111yescharacteristic
571C22C2×#137×C4111yescharacteristic
572C4—21no—
573C4—21no—
574C4—21no—
575C4—21no—
576C4—44no—
577C4—42no—
578C4—42no—
579C4—42no—
580C4—42no—
581C4—82no—
582C2—21no—
583C2—21no—
584C2—22no—
585C2—82no—
586C2—82no—
587C2C41×#161814yesdirect product factor
588C2C2×C41×#45211yescharacteristic
589C2C2×C41×#45311yescharacteristic
590C2C2×C41×#45811yescharacteristic
subgroupG/H
center, socleC23×C41#120
commutator, Frattini, cosocleC22×C4C24×C41
prime radicalC2×C41×#538C2
LCSG ▷ C22×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. C2×C41×#484C2semidirect
3. C2×C41×#481C2semidirect
4. C2×C41×#399C2semidirect
5. C41×#1618C2direct (N × H)
6. C2×C41×#328C2semidirect
7. C2×C41×#327C2semidirect
8. C2×C41×#323C2semidirect
26. C41×#484C22semidirect
28. C41×#481C22semidirect
36. C41×#399C22semidirect
38. C41×#328C22semidirect
39. C41×#327C22semidirect
40. C41×#323C22semidirect
252. C2×#1618C41direct (N × H)
288. C2×#484C2×C41semidirect
289. C2×#481C2×C41semidirect
290. C2×#399C2×C41semidirect
291. #1618C2×C41direct (N × H)
292. C2×#328C2×C41semidirect
293. C2×#327C2×C41semidirect
294. C2×#323C2×C41semidirect
300. C2×C41#1618direct (N × H)
321. #484C22×C41semidirect
323. #481C22×C41semidirect
331. #399C22×C41semidirect
333. #328C22×C41semidirect
334. #327C22×C41semidirect
335. #323C22×C41semidirect
336. C41C2×#1618direct (N × H)
587. C2C41×#1618direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C41×#5382
C2×C41×#4842
C2×C41×#4812
C2×C41×#3992
C41×#16182
C2×C41×#3282
C2×C41×#3272
C2×C41×#3232
C2×#161841