Finite Group Databasebeta

← C41×#21076 #23797277

Subgroups — C41×#21076 #23797277

Order 10496.

1022 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#428C211yesmaximal, characteristic, complemented
2C41×#2896C211yesmaximal, characteristic
3C2×C41×#417C211yesmaximal, characteristic
4C2×C41×#413C211yesmaximal, characteristic
5C41×#2873C211yesmaximal, characteristic, complemented
6C41×#1931C214yesmaximal, complemented
7C41×#1930C214yesmaximal, complemented
8C2×C41×#343C211yesmaximal, characteristic, complemented
9C41×#1738C211yesmaximal, characteristic, complemented
10C22×#41×C41C2211yescharacteristic
11C22×M16×C41C2211yescharacteristic
12C22×M16×C41C2211yescharacteristic
13C22×M16×C41C2211yescharacteristic
14C22×M16×C41C2211yescharacteristic
15C2×#117×C41C2211yescharacteristic
16C22×C4⋊C4×C41C2211yescharacteristic
17C41×#428—22no—
18C41×#428C2214yes—
19C2×#107×C41—21no—
20C2×#106×C41—21no—
21C41×#419C2212yes—
22C41×#418C2212yes—
23C41×#417—22no—
24C41×#417—22no—
25C41×#417—21no—
26C41×#417—21no—
27C41×#416—22no—
28C2×#103×C41C2212yes—
29C2×#102×C41C2212yes—
30C41×#413C418yescomplemented
31C2×#101×C41C2212yes—
32C2×#100×C41C2212yes—
33C41×#405—22no—
34C41×#405C2214yes—
35C4×M16×C41—22no—
36C41×#343C2214yes—
37C41×#341C2214yes—
38C2×#41×C41—22no—
39C2×#41×C41—21no—
40C2×#41×C41—21no—
41C2×#41×C41—21no—
42C2×#41×C41—21no—
43C2×#41×C41—22no—
44C2×#41×C41—22no—
45C2×#41×C41C2×C414yes—
46C22×Q8×C41C2311yescharacteristic
47C22×D4×C41—21no—
48C22×D4×C41C2311yescharacteristic
49C23×C4×C41—21no—
50C23×C4×C41—21no—
51C23×C4×C41C2311yescharacteristic
52C2×M16×C41—21no—
53C2×M16×C41—21no—
54C2×M16×C41—22no—
55C2×M16×C41—22no—
56C2×M16×C41—22no—
57C2×M16×C41—22no—
58C2×M16×C41—21no—
59C2×M16×C41—22no—
60C2×M16×C41—22no—
61C2×M16×C41C2×C414yes—
62C2×M16×C41C2×C414yes—
63C2×M16×C41D412yes—
64C2×M16×C41D412yes—
65C2×M16×C41C2312yes—
66C2×M16×C41C2312yes—
67C2×M16×C41C2312yes—
68C22×C8×C41—21no—
69C22×C8×C41—21no—
70C22×C8×C41—21no—
71C22×C8×C41C2312yes—
72#117×C41—21no—
73#117×C41—21no—
74#117×C41D412yes—
75#117×C41C2312yes—
76C2×C4⋊C4×C41—21no—
77C2×C4⋊C4×C41—21no—
78C2×C4⋊C4×C41—21no—
79C2×C4⋊C4×C41—21no—
80C2×C4⋊C4×C41—21no—
81C2×C4⋊C4×C41D411yescharacteristic
82C2×C4⋊C4×C41D411yescharacteristic
83C2×C4⋊C4×C41C2312yes—
84C2×C22⋊C4×C41—21no—
85C2×C42×C41—21no—
86#107×C41—24no—
87#106×C41—24no—
88#103×C41—24no—
89#103×C41—22no—
90#103×C41—22no—
91#102×C41—24no—
92#102×C41—22no—
93#102×C41—22no—
94#101×C41C2×C418yescomplemented
95#100×C41C2×C418yescomplemented
96#97×C41—24no—
97C4×C8×C41—24no—
98C24×C41—21no—
99C24×C41#4111yescharacteristic
100#41×C41—24no—
101#41×C41—24no—
102#41×C41—24no—
103#41×C41—24no—
104#41×C41—42no—
105#41×C41—42no—
106#41×C41—42no—
107#41×C41—42no—
108C2×Q8×C41—21no—
109C2×Q8×C41—21no—
110C2×Q8×C41—21no—
111C2×Q8×C41—21no—
112C2×Q8×C41—21no—
113C2×Q8×C41C22×C412yes—
114C2×D4×C41—24no—
115C2×D4×C41—21no—
116C2×D4×C41—21no—
117C2×D4×C41—21no—
118C2×D4×C41—21no—
119C2×D4×C41—21no—
120C2×D4×C41—41no—
121C2×D4×C41—41no—
122C2×D4×C41—42no—
123C2×D4×C41C22×C412yes—
124C22×C4×C41—21no—
125C22×C4×C41—21no—
126C22×C4×C41—21no—
127C22×C4×C41—24no—
128C22×C4×C41—22no—
129C22×C4×C41—41no—
130C22×C4×C41—41no—
131C22×C4×C41—42no—
132C22×C4×C41—41no—
133C22×C4×C41—41no—
134C22×C4×C41—82no—
135C22×C4×C41C22×C412yes—
136C22×C4×C41C2×D411yescharacteristic
137C22×C4×C41C2×D411yescharacteristic
138C22×C4×C41C2×D411yescharacteristic
139C22×C4×C41C2×D411yescharacteristic
140C22×C4×C41#4111yescharacteristic
141C22×C4×C41#4112yes—
142C22×C4×C41#4112yes—
143C22×C4×C41#4112yes—
144C22×C4×C41C2411yescharacteristic
145M16×C41—24no—
146M16×C41—24no—
147M16×C41—24no—
148M16×C41—24no—
149M16×C41—22no—
150M16×C41—22no—
151M16×C41—22no—
152M16×C41—22no—
153M16×C41—42no—
154M16×C41C22×C414yes—
155M16×C41C22×C414yes—
156C2×C8×C41—24no—
157C2×C8×C41—24no—
158C2×C8×C41—22no—
159C2×C8×C41—22no—
160C2×C8×C41—22no—
161C2×C8×C41—22no—
162C2×C8×C41—22no—
163C2×C8×C41—42no—
164C2×C8×C41C2×D414yes—
165C4⋊C4×C41—21no—
166C4⋊C4×C41—21no—
167C4⋊C4×C41—22no—
168C4⋊C4×C41—22no—
169C4⋊C4×C41—41no—
170C4⋊C4×C41—41no—
171C4⋊C4×C41C2×D412yes—
172C4⋊C4×C41C2×D412yes—
173C22⋊C4×C41—22no—
174C22⋊C4×C41—22no—
175C42×C41—22no—
176C42×C41—22no—
177C23×C41—22no—
178C23×C41—41no—
179C23×C41—41no—
180C23×C41—41no—
181C23×C41—41no—
182C23×C41—81no—
183C23×C41—81no—
184C23×C41#11712yes—
185C23×C41#12111yescharacteristic
186C23×C41#12111yescharacteristic
187C23×C41#12612yes—
188C23×C41C2×#4111yescharacteristic
189Q8×C41—22no—
190Q8×C41—22no—
191Q8×C41—41no—
192Q8×C41—41no—
193D4×C41—22no—
194D4×C41—22no—
195D4×C41—44no—
196D4×C41—44no—
197D4×C41—41no—
198D4×C41—41no—
199C2×C4×C41—22no—
200C2×C4×C41—22no—
201C2×C4×C41—22no—
202C2×C4×C41—41no—
203C2×C4×C41—41no—
204C2×C4×C41—44no—
205C2×C4×C41—44no—
206C2×C4×C41—42no—
207C2×C4×C41—81no—
208C2×C4×C41—81no—
209C2×C4×C41—82no—
210C2×C4×C41—82no—
211C2×C4×C41—82no—
212C2×C4×C41#11712yes—
213C2×C4×C41C4×D412yes—
214C2×C4×C41C4×D412yes—
215C2×C4×C41C4×D412yes—
216C2×C4×C41C4×D412yes—
217C2×C4×C41#12111yescharacteristic
218C2×C4×C41#12111yescharacteristic
219C2×C4×C41#12312yes—
220C2×C4×C41#12312yes—
221C2×C4×C41#12412yes—
222C2×C4×C41#12412yes—
223C2×C4×C41#12612yes—
224C2×C4×C41C23×C411yescharacteristic
225C2×C4×C41C22×D411yescharacteristic
226C2×C4×C41C22×D411yescharacteristic
227C2×C4×C41C2×#4111yescharacteristic
228C2×C4×C41C2×#4111yescharacteristic
229C2×C4×C41C2×#4111yescharacteristic
230C8×C41—24no—
231C8×C41—24no—
232C8×C41—24no—
233C8×C41—42no—
234#21076C4111yesmaximal, characteristic, direct product factor, Sylow
235C22×C41—21no—
236C22×C41—21no—
237C22×C41—21no—
238C22×C41—21no—
239C22×C41—21no—
240C22×C41—21no—
241C22×C41—42no—
242C22×C41—42no—
243C22×C41—42no—
244C22×C41—82no—
245C22×C41—82no—
246C22×C41—81no—
247C22×C41—81no—
248C22×C41#38812yes—
249C22×C41#38812yes—
250C22×C41C2×#11711yescharacteristic
251C22×C41C2×#12111yescharacteristic
252C22×C41C2×#12611yescharacteristic
253C4×C41—42no—
254C4×C41—42no—
255C4×C41—42no—
256C4×C41—82no—
257C4×C41#38812yes—
258C4×C41#38812yes—
259C4×C41C2×C4×D411yescharacteristic
260C4×C41C2×C4×D411yescharacteristic
261C4×C41C2×#12311yescharacteristic
262C4×C41C2×#12411yescharacteristic
263C2×#428C2×C4111yescharacteristic, complemented
264#2896C2×C4111yescharacteristic
265C2×#417C2×C4111yescharacteristic
266C2×#413C2×C4111yescharacteristic
267#2873C2×C4111yescharacteristic, complemented
268#1931C2×C4114yescomplemented
269#1930C2×C4114yescomplemented
270C2×#343C2×C4111yescharacteristic, complemented
271#1738C2×C4111yescharacteristic, complemented
272C2×C41—21no—
273C2×C41—21no—
274C2×C41—22no—
275C2×C41—22no—
276C2×C41—82no—
277C2×C41C2×#38811yescharacteristic
278C2×C41#306811yescharacteristic
279C2×C41#306911yescharacteristic
280C22×#41C22×C4111yescharacteristic
281C22×M16C22×C4111yescharacteristic
282C22×M16C22×C4111yescharacteristic
283C22×M16C22×C4111yescharacteristic
284C22×M16C22×C4111yescharacteristic
285C2×#117C22×C4111yescharacteristic
286C22×C4⋊C4C22×C4111yescharacteristic
287#428—22no—
288#428C22×C4114yes—
289C2×#107—21no—
290C2×#106—21no—
291#419C22×C4112yes—
292#418C22×C4112yes—
293#417—22no—
294#417—22no—
295#417—21no—
296#417—21no—
297#416—22no—
298C2×#103C22×C4112yes—
299C2×#102C22×C4112yes—
300#413C4×C4118yescomplemented
301C2×#101C22×C4112yes—
302C2×#100C22×C4112yes—
303#405—22no—
304#405C22×C4114yes—
305C4×M16—22no—
306#343C22×C4114yes—
307#341C22×C4114yes—
308C41#2107611yescharacteristic, direct product factor, Sylow
309C2×#41—22no—
310C2×#41—21no—
311C2×#41—21no—
312C2×#41—21no—
313C2×#41—21no—
314C2×#41—22no—
315C2×#41—22no—
316C2×#41C2×C4×C4114yes—
317C22×Q8C23×C4111yescharacteristic
318C22×D4—21no—
319C22×D4C23×C4111yescharacteristic
320C23×C4—21no—
321C23×C4—21no—
322C23×C4C23×C4111yescharacteristic
323C2×M16—21no—
324C2×M16—21no—
325C2×M16—22no—
326C2×M16—22no—
327C2×M16—22no—
328C2×M16—22no—
329C2×M16—21no—
330C2×M16—22no—
331C2×M16—22no—
332C2×M16C2×C4×C4114yes—
333C2×M16C2×C4×C4114yes—
334C2×M16D4×C4112yes—
335C2×M16D4×C4112yes—
336C2×M16C23×C4112yes—
337C2×M16C23×C4112yes—
338C2×M16C23×C4112yes—
339C22×C8—21no—
340C22×C8—21no—
341C22×C8—21no—
342C22×C8C23×C4112yes—
343#117—21no—
344#117—21no—
345#117D4×C4112yes—
346#117C23×C4112yes—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4D4×C4111yescharacteristic
353C2×C4⋊C4D4×C4111yescharacteristic
354C2×C4⋊C4C23×C4112yes—
355C2×C22⋊C4—21no—
356C2×C42—21no—
357#107—24no—
358#106—24no—
359#103—24no—
360#103—22no—
361#103—22no—
362#102—24no—
363#102—22no—
364#102—22no—
365#101C2×C4×C4118yescomplemented
366#100C2×C4×C4118yescomplemented
367#97—24no—
368C4×C8—24no—
369C24—21no—
370C24#41×C4111yescharacteristic
371#41—24no—
372#41—24no—
373#41—24no—
374#41—24no—
375#41—42no—
376#41—42no—
377#41—42no—
378#41—42no—
379C2×Q8—21no—
380C2×Q8—21no—
381C2×Q8—21no—
382C2×Q8—21no—
383C2×Q8—21no—
384C2×Q8C22×C4×C4112yes—
385C2×D4—24no—
386C2×D4—21no—
387C2×D4—21no—
388C2×D4—21no—
389C2×D4—21no—
390C2×D4—21no—
391C2×D4—41no—
392C2×D4—41no—
393C2×D4—42no—
394C2×D4C22×C4×C4112yes—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—24no—
399C22×C4—22no—
400C22×C4—41no—
401C22×C4—41no—
402C22×C4—42no—
403C22×C4—41no—
404C22×C4—41no—
405C22×C4—82no—
406C22×C4C22×C4×C4112yes—
407C22×C4C2×D4×C4111yescharacteristic
408C22×C4C2×D4×C4111yescharacteristic
409C22×C4C2×D4×C4111yescharacteristic
410C22×C4C2×D4×C4111yescharacteristic
411C22×C4#41×C4111yescharacteristic
412C22×C4#41×C4112yes—
413C22×C4#41×C4112yes—
414C22×C4#41×C4112yes—
415C22×C4C24×C4111yescharacteristic
416M16—24no—
417M16—24no—
418M16—24no—
419M16—24no—
420M16—22no—
421M16—22no—
422M16—22no—
423M16—22no—
424M16—42no—
425M16C22×C4×C4114yes—
426M16C22×C4×C4114yes—
427C2×C8—24no—
428C2×C8—24no—
429C2×C8—22no—
430C2×C8—22no—
431C2×C8—22no—
432C2×C8—22no—
433C2×C8—22no—
434C2×C8—42no—
435C2×C8C2×D4×C4114yes—
436C4⋊C4—21no—
437C4⋊C4—21no—
438C4⋊C4—22no—
439C4⋊C4—22no—
440C4⋊C4—41no—
441C4⋊C4—41no—
442C4⋊C4C2×D4×C4112yes—
443C4⋊C4C2×D4×C4112yes—
444C22⋊C4—22no—
445C22⋊C4—22no—
446C42—22no—
447C42—22no—
448C23—22no—
449C23—41no—
450C23—41no—
451C23—41no—
452C23—41no—
453C23—81no—
454C23—81no—
455C23#117×C4112yes—
456C23#121×C4111yescharacteristic
457C23#121×C4111yescharacteristic
458C23#126×C4112yes—
459C23C2×#41×C4111yescharacteristic
460Q8—22no—
461Q8—22no—
462Q8—41no—
463Q8—41no—
464D4—22no—
465D4—22no—
466D4—44no—
467D4—44no—
468D4—41no—
469D4—41no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—44no—
476C2×C4—44no—
477C2×C4—42no—
478C2×C4—81no—
479C2×C4—81no—
480C2×C4—82no—
481C2×C4—82no—
482C2×C4—82no—
483C2×C4#117×C4112yes—
484C2×C4C4×D4×C4112yes—
485C2×C4C4×D4×C4112yes—
486C2×C4C4×D4×C4112yes—
487C2×C4C4×D4×C4112yes—
488C2×C4#121×C4111yescharacteristic
489C2×C4#121×C4111yescharacteristic
490C2×C4#123×C4112yes—
491C2×C4#123×C4112yes—
492C2×C4#124×C4112yes—
493C2×C4#124×C4112yes—
494C2×C4#126×C4112yes—
495C2×C4C23×C4×C4111yescharacteristic
496C2×C4C22×D4×C4111yescharacteristic
497C2×C4C22×D4×C4111yescharacteristic
498C2×C4C2×#41×C4111yescharacteristic
499C2×C4C2×#41×C4111yescharacteristic
500C2×C4C2×#41×C4111yescharacteristic
501C8—24no—
502C8—24no—
503C8—24no—
504C8—42no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—42no—
512C22—42no—
513C22—42no—
514C22—82no—
515C22—82no—
516C22—81no—
517C22—81no—
518C22C41×#38812yes—
519C22C41×#38812yes—
520C22C2×#117×C4111yescharacteristic
521C22C2×#121×C4111yescharacteristic
522C22C2×#126×C4111yescharacteristic
523C4—42no—
524C4—42no—
525C4—42no—
526C4—82no—
527C4C41×#38812yes—
528C4C41×#38812yes—
529C4C2×C4×D4×C4111yescharacteristic
530C4C2×C4×D4×C4111yescharacteristic
531C4C2×#123×C4111yescharacteristic
532C4C2×#124×C4111yescharacteristic
533C2—21no—
534C2—21no—
535C2—22no—
536C2—22no—
537C2—82no—
538C2C2×C41×#38811yescharacteristic
539C2C41×#306811yescharacteristic
540C2C41×#306911yescharacteristic
subgroupG/H
center, socleC22×C41C2×#121
commutatorC2×C4C23×C4×C41
Frattini, cosocleC22×C4C24×C41
prime radicalC22×#41×C41C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C41 ◁ C23×C4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C41×#428C2semidirect
5. C41×#2873C2semidirect
6. C41×#1931C2semidirect
7. C41×#1930C2semidirect
8. C2×C41×#343C2semidirect
9. C41×#1738C2semidirect
30. C41×#413C4semidirect
94. #101×C41C2×C4semidirect
95. #100×C41C2×C4semidirect
234. #21076C41direct (N × H)
263. C2×#428C2×C41semidirect
267. #2873C2×C41semidirect
268. #1931C2×C41semidirect
269. #1930C2×C41semidirect
270. C2×#343C2×C41semidirect
271. #1738C2×C41semidirect
300. #413C4×C41semidirect
308. C41#21076direct (N × H)
365. #101C2×C4×C41semidirect
366. #100C2×C4×C41semidirect

Maximal subgroups

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

subgroupindex
C2×C41×#4282
C41×#28962
C2×C41×#4172
C2×C41×#4132
C41×#28732
C41×#19312
C41×#19302
C2×C41×#3432
C41×#17382
#2107641