Finite Group Databasebeta

← C41×#29170 #23805371

Subgroups — C41×#29170 #23805371

Order 10496.

728 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#2628C211yesmaximal, characteristic
2C41×#2323C211yesmaximal, characteristic
3C41×#2101C211yesmaximal, characteristic, complemented
4C41×#2097C211yesmaximal, characteristic, complemented
5C41×#2058C211yesmaximal, characteristic, complemented
6C41×#2024C211yesmaximal, characteristic, complemented
7C41×#1921C211yesmaximal, characteristic, complemented
8C41×#1920C211yesmaximal, characteristic, complemented
9C41×#1894C211yesmaximal, characteristic
10C41×#1892C211yesmaximal, characteristic
11C41×#1865C211yesmaximal, characteristic, complemented
12C41×#1865C211yesmaximal, characteristic, complemented
13C41×#1809C211yesmaximal, characteristic
14C41×#1807C211yesmaximal, characteristic
15C41×#1729C211yesmaximal, characteristic
16C22×M16×C41C2211yescharacteristic
17C23×C8×C41C2211yescharacteristic
18C2×C4⋊Q8×C41C2211yescharacteristic
19C2×C22⋊Q8×C41C2211yescharacteristic
20C2×C4×Q8×C41C2211yescharacteristic
21C2×#117×C41C2211yescharacteristic
22C2×#107×C41C2211yescharacteristic
23C2×#106×C41C2211yescharacteristic
24C2×#106×C41C2211yescharacteristic
25C2×#106×C41C2211yescharacteristic
26C2×#103×C41C2211yescharacteristic
27C2×#103×C41C2211yescharacteristic
28C2×#103×C41C2211yescharacteristic
29C2×#103×C41C2211yescharacteristic
30C41×#400—21no—
31C41×#399—21no—
32C41×#395—21no—
33C41×#393—21no—
34C41×#391C2211yescharacteristic
35C41×#389—21no—
36C41×#389C2211yescharacteristic
37C41×#389C2211yescharacteristic
38C41×#389C2211yescharacteristic
39C41×#388—21no—
40C41×#388—21no—
41C41×#387—21no—
42C41×#382C2211yescharacteristic
43C41×#380C2211yescharacteristic
44C41×#380C2211yescharacteristic
45C41×#380C2211yescharacteristic
46C4×C4⋊C4×C41C2211yescharacteristic
47C41×#340C2211yescharacteristic
48C41×#340C2211yescharacteristic
49C41×#340C2211yescharacteristic
50C41×#340C2211yescharacteristic
51C41×#340C2211yescharacteristic
52C41×#340C2211yescharacteristic
53C41×#340C2211yescharacteristic
54C41×#340C2211yescharacteristic
55C41×#336C2211yescharacteristic
56C41×#336C2211yescharacteristic
57C41×#336C2211yescharacteristic
58C41×#336C2211yescharacteristic
59C22×Q8×C41—21no—
60C22×Q8×C41C2311yescharacteristic
61C23×C4×C41C2311yescharacteristic
62C2×M16×C41—22no—
63C2×M16×C41—22no—
64C2×M16×C41—41no—
65C22×C8×C41—22no—
66C22×C8×C41—22no—
67C22×C8×C41—41no—
68C22×C8×C41C2311yescharacteristic
69C22×C8×C41C2311yescharacteristic
70C22×C8×C41C2311yescharacteristic
71C22×C8×C41C2311yescharacteristic
72C4⋊Q8×C41—41no—
73C4⋊Q8×C41—41no—
74C22⋊Q8×C41—22no—
75C22⋊Q8×C41Q814yescomplemented
76C4×Q8×C41—41no—
77C4×Q8×C41—41no—
78#117×C41—41no—
79#117×C41—41no—
80C2×C4⋊C4×C41—21no—
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×C41D411yescharacteristic
87C2×C4⋊C4×C41D411yescharacteristic
88C2×C4⋊C4×C41C2311yescharacteristic
89C2×C4⋊C4×C41C2311yescharacteristic
90C2×C4⋊C4×C41C2311yescharacteristic
91C2×C4⋊C4×C41C2311yescharacteristic
92C2×C4⋊C4×C41C2311yescharacteristic
93C2×C4⋊C4×C41C2311yescharacteristic
94C2×C4⋊C4×C41C2311yescharacteristic
95C2×C22⋊C4×C41—21no—
96C2×C22⋊C4×C41—21no—
97C2×C22⋊C4×C41—21no—
98C2×C22⋊C4×C41—21no—
99C2×C22⋊C4×C41D411yescharacteristic
100C2×C22⋊C4×C41D411yescharacteristic
101C2×C42×C41—21no—
102C2×C42×C41—21no—
103C2×C42×C41C2311yescharacteristic
104C2×C42×C41C2311yescharacteristic
105#107×C41—22no—
106#106×C41—22no—
107#106×C41—41no—
108#106×C41—41no—
109#103×C41—22no—
110#103×C41—22no—
111#103×C41—41no—
112#103×C41—41no—
113#95×C41—21no—
114#95×C41—21no—
115#95×C41—21no—
116#95×C41—21no—
117#95×C41—21no—
118#95×C41—21no—
119#95×C41—21no—
120#95×C41—21no—
121#95×C41—21no—
122#95×C41—21no—
123#95×C41—21no—
124C24×C41C2×D411yescharacteristic
125C2×Q8×C41—21no—
126C2×Q8×C41—21no—
127C2×Q8×C41—21no—
128C2×Q8×C41—21no—
129C2×Q8×C41—21no—
130C2×Q8×C41—42no—
131C2×Q8×C41—81no—
132C2×Q8×C41—81no—
133C2×Q8×C41C2×Q812yes—
134C22×C4×C41—21no—
135C22×C4×C41—21no—
136C22×C4×C41—21no—
137C22×C4×C41—21no—
138C22×C4×C41—21no—
139C22×C4×C41—21no—
140C22×C4×C41—21no—
141C22×C4×C41—21no—
142C22×C4×C41—21no—
143C22×C4×C41—21no—
144C22×C4×C41—21no—
145C22×C4×C41—21no—
146C22×C4×C41C2×D411yescharacteristic
147C22×C4×C41C2×D411yescharacteristic
148C22×C4×C41C2×D411yescharacteristic
149C22×C4×C41C2×D411yescharacteristic
150C22×C4×C41C2×D411yescharacteristic
151C22×C4×C41C2×Q812yes—
152C22×C4×C41#4112yes—
153C22×C4×C41C2411yescharacteristic
154M16×C41—44no—
155C2×C8×C41—21no—
156C2×C8×C41—21no—
157C2×C8×C41—21no—
158C2×C8×C41—21no—
159C2×C8×C41—21no—
160C2×C8×C41—21no—
161C2×C8×C41—21no—
162C2×C8×C41—21no—
163C2×C8×C41—21no—
164C2×C8×C41—21no—
165C2×C8×C41—44no—
166C2×C8×C41#4112yes—
167C2×C8×C41#4112yes—
168C4⋊C4×C41—24no—
169C4⋊C4×C41—21no—
170C4⋊C4×C41—21no—
171C4⋊C4×C41—21no—
172C4⋊C4×C41—21no—
173C4⋊C4×C41—21no—
174C4⋊C4×C41—21no—
175C4⋊C4×C41—21no—
176C4⋊C4×C41—21no—
177C4⋊C4×C41—21no—
178C4⋊C4×C41—21no—
179C4⋊C4×C41—21no—
180C4⋊C4×C41—21no—
181C4⋊C4×C41—21no—
182C4⋊C4×C41—41no—
183C4⋊C4×C41—41no—
184C4⋊C4×C41—42no—
185C4⋊C4×C41—42no—
186C4⋊C4×C41—81no—
187C4⋊C4×C41—81no—
188C4⋊C4×C41—81no—
189C4⋊C4×C41C2×Q812yes—
190C22⋊C4×C41—24no—
191C22⋊C4×C41—41no—
192C22⋊C4×C41—41no—
193C22⋊C4×C41—81no—
194C22⋊C4×C41—81no—
195C22⋊C4×C41—81no—
196C42×C41—21no—
197C42×C41—21no—
198C42×C41—21no—
199C42×C41—21no—
200C42×C41—42no—
201C42×C41—81no—
202C23×C41—21no—
203C23×C41—21no—
204C23×C41—21no—
205C23×C41—21no—
206C23×C41—21no—
207C23×C41—21no—
208C23×C41C22⋊Q812yes—
209C23×C41C22×D411yescharacteristic
210Q8×C41—22no—
211Q8×C41—22no—
212Q8×C41—41no—
213Q8×C41—41no—
214Q8×C41—84no—
215C2×C4×C41—21no—
216C2×C4×C41—21no—
217C2×C4×C41—22no—
218C2×C4×C41—22no—
219C2×C4×C41—22no—
220C2×C4×C41—22no—
221C2×C4×C41—22no—
222C2×C4×C41—22no—
223C2×C4×C41—21no—
224C2×C4×C41—21no—
225C2×C4×C41—21no—
226C2×C4×C41—21no—
227C2×C4×C41—21no—
228C2×C4×C41—21no—
229C2×C4×C41—21no—
230C2×C4×C41—21no—
231C2×C4×C41—21no—
232C2×C4×C41—21no—
233C2×C4×C41—21no—
234C2×C4×C41—21no—
235C2×C4×C41—41no—
236C2×C4×C41—41no—
237C2×C4×C41—41no—
238C2×C4×C41—41no—
239C2×C4×C41—41no—
240C2×C4×C41—41no—
241C2×C4×C41—41no—
242C2×C4×C41—41no—
243C2×C4×C41—41no—
244C2×C4×C41—41no—
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×C41C22⋊Q812yes—
258C2×C4×C41C22×Q811yescharacteristic
259C2×C4×C41C2×#4111yescharacteristic
260C2×C4×C41C2×#4111yescharacteristic
261C2×C4×C41C2×#4111yescharacteristic
262C2×C4×C41H(5,𝔽2)11yescharacteristic
263C2×C4×C41H(5,𝔽2)11yescharacteristic
264C8×C41—22no—
265C8×C41—22no—
266C8×C41—41no—
267C8×C41—41no—
268#29170C4111yesmaximal, characteristic, direct product factor, Sylow
269C22×C41—22no—
270C22×C41—22no—
271C22×C41—22no—
272C22×C41—41no—
273C22×C41—41no—
274C22×C41—41no—
275C22×C41—41no—
276C22×C41C2×C22⋊Q811yescharacteristic
277C22×C41#53211yescharacteristic
278C22×C41#53411yescharacteristic
279C22×C41#57711yescharacteristic
280C22×C41#57711yescharacteristic
281C22×C41#57711yescharacteristic
282C22×C41#57811yescharacteristic
283C4×C41—22no—
284C4×C41—42no—
285C4×C41—42no—
286C4×C41—41no—
287C4×C41—41no—
288C4×C41—41no—
289C4×C41—41no—
290C4×C41—81no—
291C4×C41—81no—
292C4×C41—81no—
293C4×C41—81no—
294C4×C41—81no—
295C4×C41—81no—
296C4×C41#55111yescharacteristic
297C4×C41#55111yescharacteristic
298C4×C41#55411yescharacteristic
299C4×C41#55411yescharacteristic
300#2628C2×C4111yescharacteristic
301#2323C2×C4111yescharacteristic
302#2101C2×C4111yescharacteristic, complemented
303#2097C2×C4111yescharacteristic, complemented
304#2058C2×C4111yescharacteristic, complemented
305#2024C2×C4111yescharacteristic, complemented
306#1921C2×C4111yescharacteristic, complemented
307#1920C2×C4111yescharacteristic, complemented
308#1894C2×C4111yescharacteristic
309#1892C2×C4111yescharacteristic
310#1865C2×C4111yescharacteristic, complemented
311#1865C2×C4111yescharacteristic, complemented
312#1809C2×C4111yescharacteristic
313#1807C2×C4111yescharacteristic
314#1729C2×C4111yescharacteristic
315C2×C41—42no—
316C2×C41#256411yescharacteristic
317C2×C41#308211yescharacteristic
318C2×C41#308411yescharacteristic
319C2×C41#317311yescharacteristic
320C2×C41#317811yescharacteristic
321C2×C41#320011yescharacteristic
322C2×C41#320111yescharacteristic
323C22×M16C22×C4111yescharacteristic
324C23×C8C22×C4111yescharacteristic
325C2×C4⋊Q8C22×C4111yescharacteristic
326C2×C22⋊Q8C22×C4111yescharacteristic
327C2×C4×Q8C22×C4111yescharacteristic
328C2×#117C22×C4111yescharacteristic
329C2×#107C22×C4111yescharacteristic
330C2×#106C22×C4111yescharacteristic
331C2×#106C22×C4111yescharacteristic
332C2×#106C22×C4111yescharacteristic
333C2×#103C22×C4111yescharacteristic
334C2×#103C22×C4111yescharacteristic
335C2×#103C22×C4111yescharacteristic
336C2×#103C22×C4111yescharacteristic
337#400—21no—
338#399—21no—
339#395—21no—
340#393—21no—
341#391C22×C4111yescharacteristic
342#389—21no—
343#389C22×C4111yescharacteristic
344#389C22×C4111yescharacteristic
345#389C22×C4111yescharacteristic
346#388—21no—
347#388—21no—
348#387—21no—
349#382C22×C4111yescharacteristic
350#380C22×C4111yescharacteristic
351#380C22×C4111yescharacteristic
352#380C22×C4111yescharacteristic
353C4×C4⋊C4C22×C4111yescharacteristic
354#340C22×C4111yescharacteristic
355#340C22×C4111yescharacteristic
356#340C22×C4111yescharacteristic
357#340C22×C4111yescharacteristic
358#340C22×C4111yescharacteristic
359#340C22×C4111yescharacteristic
360#340C22×C4111yescharacteristic
361#340C22×C4111yescharacteristic
362#336C22×C4111yescharacteristic
363#336C22×C4111yescharacteristic
364#336C22×C4111yescharacteristic
365#336C22×C4111yescharacteristic
366C41#2917011yescharacteristic, direct product factor, Sylow
367C22×Q8—21no—
368C22×Q8C23×C4111yescharacteristic
369C23×C4C23×C4111yescharacteristic
370C2×M16—22no—
371C2×M16—22no—
372C2×M16—41no—
373C22×C8—22no—
374C22×C8—22no—
375C22×C8—41no—
376C22×C8C23×C4111yescharacteristic
377C22×C8C23×C4111yescharacteristic
378C22×C8C23×C4111yescharacteristic
379C22×C8C23×C4111yescharacteristic
380C4⋊Q8—41no—
381C4⋊Q8—41no—
382C22⋊Q8—22no—
383C22⋊Q8Q8×C4114yescomplemented
384C4×Q8—41no—
385C4×Q8—41no—
386#117—41no—
387#117—41no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4D4×C4111yescharacteristic
395C2×C4⋊C4D4×C4111yescharacteristic
396C2×C4⋊C4C23×C4111yescharacteristic
397C2×C4⋊C4C23×C4111yescharacteristic
398C2×C4⋊C4C23×C4111yescharacteristic
399C2×C4⋊C4C23×C4111yescharacteristic
400C2×C4⋊C4C23×C4111yescharacteristic
401C2×C4⋊C4C23×C4111yescharacteristic
402C2×C4⋊C4C23×C4111yescharacteristic
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4D4×C4111yescharacteristic
408C2×C22⋊C4D4×C4111yescharacteristic
409C2×C42—21no—
410C2×C42—21no—
411C2×C42C23×C4111yescharacteristic
412C2×C42C23×C4111yescharacteristic
413#107—22no—
414#106—22no—
415#106—41no—
416#106—41no—
417#103—22no—
418#103—22no—
419#103—41no—
420#103—41no—
421#95—21no—
422#95—21no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—21no—
431#95—21no—
432C24C2×D4×C4111yescharacteristic
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—42no—
439C2×Q8—81no—
440C2×Q8—81no—
441C2×Q8C2×Q8×C4112yes—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4C2×D4×C4111yescharacteristic
455C22×C4C2×D4×C4111yescharacteristic
456C22×C4C2×D4×C4111yescharacteristic
457C22×C4C2×D4×C4111yescharacteristic
458C22×C4C2×D4×C4111yescharacteristic
459C22×C4C2×Q8×C4112yes—
460C22×C4#41×C4112yes—
461C22×C4C24×C4111yescharacteristic
462M16—44no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—44no—
474C2×C8#41×C4112yes—
475C2×C8#41×C4112yes—
476C4⋊C4—24no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—41no—
491C4⋊C4—41no—
492C4⋊C4—42no—
493C4⋊C4—42no—
494C4⋊C4—81no—
495C4⋊C4—81no—
496C4⋊C4—81no—
497C4⋊C4C2×Q8×C4112yes—
498C22⋊C4—24no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—81no—
502C22⋊C4—81no—
503C22⋊C4—81no—
504C42—21no—
505C42—21no—
506C42—21no—
507C42—21no—
508C42—42no—
509C42—81no—
510C23—21no—
511C23—21no—
512C23—21no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23C22⋊Q8×C4112yes—
517C23C22×D4×C4111yescharacteristic
518Q8—22no—
519Q8—22no—
520Q8—41no—
521Q8—41no—
522Q8—84no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4C22⋊Q8×C4112yes—
566C2×C4C22×Q8×C4111yescharacteristic
567C2×C4C2×#41×C4111yescharacteristic
568C2×C4C2×#41×C4111yescharacteristic
569C2×C4C2×#41×C4111yescharacteristic
570C2×C4H(5,𝔽2)×C4111yescharacteristic
571C2×C4H(5,𝔽2)×C4111yescharacteristic
572C8—22no—
573C8—22no—
574C8—41no—
575C8—41no—
576C22—22no—
577C22—22no—
578C22—22no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22C2×C22⋊Q8×C4111yescharacteristic
584C22C41×#53211yescharacteristic
585C22C41×#53411yescharacteristic
586C22C41×#57711yescharacteristic
587C22C41×#57711yescharacteristic
588C22C41×#57711yescharacteristic
589C22C41×#57811yescharacteristic
590C4—22no—
591C4—42no—
592C4—42no—
593C4—41no—
594C4—41no—
595C4—41no—
596C4—41no—
597C4—81no—
598C4—81no—
599C4—81no—
600C4—81no—
601C4—81no—
602C4—81no—
603C4C41×#55111yescharacteristic
604C4C41×#55111yescharacteristic
605C4C41×#55411yescharacteristic
606C4C41×#55411yescharacteristic
607C2—42no—
608C2C41×#256411yescharacteristic
609C2C41×#308211yescharacteristic
610C2C41×#308411yescharacteristic
611C2C41×#317311yescharacteristic
612C2C41×#317811yescharacteristic
613C2C41×#320011yescharacteristic
614C2C41×#320111yescharacteristic
subgroupG/H
center, socleC23×C41C22×D4
commutator, Frattini, cosocleC22×C4C24×C41
prime radicalC24×C41C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C41 ◁ C2×#117×C41 ◁ G

Complements

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

NH ≅ G/Ntype
3. C41×#2101C2semidirect
4. C41×#2097C2semidirect
5. C41×#2058C2semidirect
6. C41×#2024C2semidirect
7. C41×#1921C2semidirect
8. C41×#1920C2semidirect
11. C41×#1865C2semidirect
12. C41×#1865C2semidirect
75. C22⋊Q8×C41Q8semidirect
268. #29170C41direct (N × H)
302. #2101C2×C41semidirect
303. #2097C2×C41semidirect
304. #2058C2×C41semidirect
305. #2024C2×C41semidirect
306. #1921C2×C41semidirect
307. #1920C2×C41semidirect
310. #1865C2×C41semidirect
311. #1865C2×C41semidirect
366. C41#29170direct (N × H)
383. C22⋊Q8Q8×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#26282
C41×#23232
C41×#21012
C41×#20972
C41×#20582
C41×#20242
C41×#19212
C41×#19202
C41×#18942
C41×#18922
C41×#18652
C41×#18092
C41×#18072
C41×#17292
#2917041