Finite Group Databasebeta

← C41×#25159 #23801360

Subgroups — C41×#25159 #23801360

Order 10496.

1212 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#460C211yesmaximal, characteristic, complemented
2C2×C41×#449C211yesmaximal, characteristic, complemented
3C2×C41×#449C211yesmaximal, characteristic, complemented
4C2×C4×SD16×C41C211yesmaximal, characteristic, complemented
5C41×#2428C211yesmaximal, characteristic, complemented
6C41×#2341C211yesmaximal, characteristic, complemented
7C41×#2065C211yesmaximal, characteristic, complemented
8C41×#2034C211yesmaximal, characteristic, complemented
9C41×#2033C211yesmaximal, characteristic, complemented
10C41×#2011C211yesmaximal, characteristic, complemented
11C41×#1970C211yesmaximal, characteristic, complemented
12C41×#1923C211yesmaximal, characteristic, complemented
13C41×#1880C211yesmaximal, characteristic, complemented
14C41×#1879C211yesmaximal, characteristic, complemented
15C41×#1863C211yesmaximal, characteristic, complemented
16C22×#41×C41C2211yescharacteristic
17C22×SD16×C41C2211yescharacteristic
18C22×SD16×C41C2211yescharacteristic
19C22×D8×C41C2211yescharacteristic
20C22×D8×C41C2211yescharacteristic
21C2×#127×C41C2211yescharacteristic
22C2×#121×C41—21no—
23C2×#121×C41C2211yescharacteristic
24C2×#121×C41C2211yescharacteristic
25C2×C4×Q8×C41C2211yescharacteristic
26C2×C4×Q8×C41C2211yescharacteristic
27C2×C4×D4×C41C2211yescharacteristic
28C41×#460—24no—
29C41×#449—24no—
30C41×#449—24no—
31C4×SD16×C41—24no—
32C2×#107×C41C2211yescharacteristic
33C2×#106×C41C2211yescharacteristic
34C2×C4⋊C8×C41C2211yescharacteristic
35C2×#103×C41C2211yescharacteristic
36C2×#103×C41C2211yescharacteristic
37C2×#102×C41C2211yescharacteristic
38C2×#102×C41C2211yescharacteristic
39C2×#102×C41C2211yescharacteristic
40C2×#102×C41C2211yescharacteristic
41C2×#102×C41C2211yescharacteristic
42C2×#102×C41C2211yescharacteristic
43C2×C22⋊C8×C41C2211yescharacteristic
44C2×C22⋊C8×C41C2211yescharacteristic
45C2×C4×C8×C41C2211yescharacteristic
46C41×#394—21no—
47C41×#392—21no—
48C41×#390—21no—
49C41×#390—21no—
50C41×#390C2211yescharacteristic
51C41×#390C2211yescharacteristic
52C41×#390C2211yescharacteristic
53C41×#389C2211yescharacteristic
54C41×#386—21no—
55C41×#380—21no—
56C41×#380C2211yescharacteristic
57C4×C22⋊C4×C41—21no—
58C4×C22⋊C4×C41C2211yescharacteristic
59C41×#340C2211yescharacteristic
60C41×#340C2211yescharacteristic
61C41×#336C2211yescharacteristic
62C41×#336C2211yescharacteristic
63C2×#41×C41—22no—
64C2×#41×C41—22no—
65C2×#41×C41—22no—
66C2×#41×C41—22no—
67C2×#41×C41—41no—
68C2×#41×C41—41no—
69C22×Q8×C41C2311yescharacteristic
70C22×D4×C41—21no—
71C22×D4×C41—21no—
72C22×D4×C41—21no—
73C22×D4×C41—21no—
74C22×D4×C41—21no—
75C22×D4×C41C2311yescharacteristic
76C22×D4×C41C2311yescharacteristic
77C22×D4×C41C2311yescharacteristic
78C23×C4×C41—21no—
79C23×C4×C41—21no—
80C23×C4×C41C2311yescharacteristic
81C2×SD16×C41—22no—
82C2×SD16×C41—22no—
83C2×SD16×C41—22no—
84C2×SD16×C41—22no—
85C2×SD16×C41—22no—
86C2×SD16×C41D414yescomplemented
87C2×D8×C41—22no—
88C2×D8×C41—22no—
89C2×D8×C41—22no—
90C2×D8×C41—22no—
91C2×D8×C41—41no—
92C2×D8×C41—41no—
93C22×C8×C41C2311yescharacteristic
94C22×C8×C41C2311yescharacteristic
95C22×C8×C41C2311yescharacteristic
96C22×C8×C41C2311yescharacteristic
97#127×C41—22no—
98#127×C41—41no—
99#121×C41—22no—
100#121×C41—22no—
101#121×C41—44no—
102#121×C41—41no—
103#121×C41—41no—
104C4×Q8×C41—22no—
105C4×Q8×C41—22no—
106C4×Q8×C41—41no—
107C4×Q8×C41—41no—
108C4×D4×C41—22no—
109C4×D4×C41—41no—
110C2×C4⋊C4×C41—21no—
111C2×C4⋊C4×C41—21no—
112C2×C4⋊C4×C41—21no—
113C2×C4⋊C4×C41C2311yescharacteristic
114C2×C4⋊C4×C41C2311yescharacteristic
115C2×C4⋊C4×C41C2311yescharacteristic
116C2×C4⋊C4×C41C2311yescharacteristic
117C2×C22⋊C4×C41—21no—
118C2×C22⋊C4×C41—21no—
119C2×C22⋊C4×C41—21no—
120C2×C22⋊C4×C41—21no—
121C2×C22⋊C4×C41—21no—
122C2×C22⋊C4×C41—21no—
123C2×C22⋊C4×C41—21no—
124C2×C22⋊C4×C41—21no—
125C2×C22⋊C4×C41—21no—
126C2×C22⋊C4×C41—21no—
127C2×C22⋊C4×C41D411yescharacteristic
128C2×C22⋊C4×C41D411yescharacteristic
129C2×C42×C41—21no—
130C2×C42×C41—21no—
131C2×C42×C41C2311yescharacteristic
132C2×C42×C41C2311yescharacteristic
133#107×C41—41no—
134#106×C41—22no—
135C4⋊C8×C41—22no—
136#103×C41—22no—
137#103×C41D414yescomplemented
138#102×C41—22no—
139#102×C41—22no—
140#102×C41—22no—
141#102×C41—22no—
142#102×C41—22no—
143#102×C41—41no—
144C22⋊C8×C41—22no—
145C22⋊C8×C41—22no—
146C4×C8×C41—22no—
147#95×C41—21no—
148#95×C41—21no—
149#95×C41D411yescharacteristic
150#95×C41D411yescharacteristic
151C24×C41—21no—
152C24×C41—21no—
153C24×C41—21no—
154C24×C41C2×D411yescharacteristic
155#41×C41—44no—
156#41×C41—44no—
157#41×C41—44no—
158#41×C41—44no—
159C2×Q8×C41—21no—
160C2×Q8×C41—21no—
161C2×Q8×C41—21no—
162C2×Q8×C41C2×D412yes—
163C2×Q8×C41C2×D412yes—
164C2×Q8×C41#4112yes—
165C2×D4×C41—24no—
166C2×D4×C41—21no—
167C2×D4×C41—21no—
168C2×D4×C41—21no—
169C2×D4×C41—21no—
170C2×D4×C41—21no—
171C2×D4×C41—21no—
172C2×D4×C41—21no—
173C2×D4×C41—21no—
174C2×D4×C41—21no—
175C2×D4×C41—21no—
176C2×D4×C41—21no—
177C2×D4×C41—21no—
178C2×D4×C41—21no—
179C2×D4×C41—21no—
180C2×D4×C41—21no—
181C2×D4×C41—21no—
182C2×D4×C41—42no—
183C2×D4×C41—42no—
184C2×D4×C41—42no—
185C2×D4×C41—42no—
186C2×D4×C41—42no—
187C2×D4×C41—42no—
188C2×D4×C41—42no—
189C2×D4×C41—42no—
190C2×D4×C41—42no—
191C2×D4×C41—42no—
192C2×D4×C41—81no—
193C2×D4×C41—81no—
194C2×D4×C41—81no—
195C2×D4×C41—81no—
196C2×D4×C41C2×D412yes—
197C2×D4×C41#4112yes—
198C22×C4×C41—21no—
199C22×C4×C41—24no—
200C22×C4×C41—21no—
201C22×C4×C41—21no—
202C22×C4×C41—21no—
203C22×C4×C41—21no—
204C22×C4×C41—21no—
205C22×C4×C41—21no—
206C22×C4×C41—21no—
207C22×C4×C41—21no—
208C22×C4×C41—21no—
209C22×C4×C41—21no—
210C22×C4×C41—42no—
211C22×C4×C41—42no—
212C22×C4×C41—42no—
213C22×C4×C41—42no—
214C22×C4×C41—81no—
215C22×C4×C41C2×D411yescharacteristic
216C22×C4×C41C2×D411yescharacteristic
217C22×C4×C41C2×D411yescharacteristic
218C22×C4×C41C2×D411yescharacteristic
219C22×C4×C41C2×D411yescharacteristic
220C22×C4×C41C2411yescharacteristic
221SD16×C41—28no—
222SD16×C41—44no—
223D8×C41—44no—
224D8×C41—44no—
225C2×C8×C41—21no—
226C2×C8×C41—21no—
227C2×C8×C41—21no—
228C2×C8×C41—21no—
229C2×C8×C41—21no—
230C2×C8×C41—21no—
231C2×C8×C41—21no—
232C2×C8×C41—21no—
233C2×C8×C41—21no—
234C2×C8×C41—21no—
235C2×C8×C41C2×D412yes—
236C2×C8×C41C2×D412yes—
237C4⋊C4×C41—21no—
238C4⋊C4×C41—21no—
239C4⋊C4×C41—21no—
240C4⋊C4×C41—21no—
241C4⋊C4×C41—21no—
242C4⋊C4×C41—21no—
243C4⋊C4×C41—21no—
244C4⋊C4×C41—42no—
245C4⋊C4×C41—42no—
246C4⋊C4×C41—42no—
247C4⋊C4×C41C2×D412yes—
248C22⋊C4×C41—22no—
249C22⋊C4×C41—22no—
250C22⋊C4×C41—42no—
251C22⋊C4×C41—42no—
252C22⋊C4×C41—42no—
253C22⋊C4×C41—42no—
254C22⋊C4×C41—42no—
255C22⋊C4×C41—42no—
256C22⋊C4×C41—81no—
257C22⋊C4×C41—81no—
258C22⋊C4×C41—81no—
259C22⋊C4×C41—81no—
260C42×C41—21no—
261C42×C41—21no—
262C42×C41—21no—
263C42×C41—21no—
264C42×C41—42no—
265C42×C41—42no—
266C23×C41—21no—
267C23×C41—22no—
268C23×C41—22no—
269C23×C41—21no—
270C23×C41—21no—
271C23×C41—21no—
272C23×C41—21no—
273C23×C41—21no—
274C23×C41—21no—
275C23×C41—41no—
276C23×C41—41no—
277C23×C41—41no—
278C23×C41—41no—
279C23×C41—41no—
280C23×C41—41no—
281C23×C41—41no—
282C23×C41—41no—
283C23×C41—41no—
284C23×C41—41no—
285C23×C41—41no—
286C23×C41—41no—
287C23×C41—41no—
288C23×C41—41no—
289C23×C41—41no—
290C23×C41—41no—
291C23×C41—41no—
292C23×C41—41no—
293C23×C41—41no—
294C23×C41C22×D411yescharacteristic
295Q8×C41—22no—
296Q8×C41—22no—
297Q8×C41—22no—
298Q8×C41#12114yescomplemented
299D4×C41—22no—
300D4×C41—22no—
301D4×C41—22no—
302D4×C41—22no—
303D4×C41—48no—
304D4×C41—41no—
305D4×C41—41no—
306D4×C41—41no—
307D4×C41—41no—
308D4×C41—41no—
309D4×C41—41no—
310D4×C41—41no—
311D4×C41—41no—
312D4×C41—84no—
313D4×C41—84no—
314D4×C41—84no—
315D4×C41—84no—
316C2×C4×C41—22no—
317C2×C4×C41—21no—
318C2×C4×C41—21no—
319C2×C4×C41—22no—
320C2×C4×C41—22no—
321C2×C4×C41—21no—
322C2×C4×C41—21no—
323C2×C4×C41—21no—
324C2×C4×C41—21no—
325C2×C4×C41—21no—
326C2×C4×C41—22no—
327C2×C4×C41—21no—
328C2×C4×C41—21no—
329C2×C4×C41—21no—
330C2×C4×C41—21no—
331C2×C4×C41—21no—
332C2×C4×C41—21no—
333C2×C4×C41—48no—
334C2×C4×C41—41no—
335C2×C4×C41—41no—
336C2×C4×C41—41no—
337C2×C4×C41—41no—
338C2×C4×C41—41no—
339C2×C4×C41—41no—
340C2×C4×C41—41no—
341C2×C4×C41—41no—
342C2×C4×C41—41no—
343C2×C4×C41—41no—
344C2×C4×C41—41no—
345C2×C4×C41—41no—
346C2×C4×C41—41no—
347C2×C4×C41—41no—
348C2×C4×C41—41no—
349C2×C4×C41—84no—
350C2×C4×C41#13512yes—
351C2×C4×C41AGL(1,ℤ/8)12yes—
352C2×C4×C41C22×D411yescharacteristic
353C2×C4×C41C22×D411yescharacteristic
354C2×C4×C41C2×#4111yescharacteristic
355C2×C4×C41C2×#4111yescharacteristic
356C2×C4×C41H(5,𝔽2)11yescharacteristic
357C2×C4×C41H(5,𝔽2)11yescharacteristic
358C8×C41—22no—
359C8×C41—22no—
360C8×C41—41no—
361C8×C41—41no—
362#25159C4111yesmaximal, characteristic, direct product factor, Sylow
363C22×C41—41no—
364C22×C41—42no—
365C22×C41—41no—
366C22×C41—42no—
367C22×C41—42no—
368C22×C41—41no—
369C22×C41—42no—
370C22×C41—41no—
371C22×C41—41no—
372C22×C41—42no—
373C22×C41—42no—
374C22×C41—41no—
375C22×C41—41no—
376C22×C41—81no—
377C22×C41—81no—
378C22×C41—81no—
379C22×C41—81no—
380C22×C41—81no—
381C22×C41—81no—
382C22×C41—81no—
383C22×C41—81no—
384C22×C41—81no—
385C22×C41—81no—
386C22×C41—81no—
387C22×C41—81no—
388C22×C41—81no—
389C22×C41—81no—
390C22×C41—81no—
391C22×C41#52511yescharacteristic
392C22×C41D4211yescharacteristic
393C22×C41D4211yescharacteristic
394C22×C41C2×#13511yescharacteristic
395C22×C41C2×AGL(1,ℤ/8)11yescharacteristic
396C22×C41#57611yescharacteristic
397C22×C41#57711yescharacteristic
398C4×C41—24no—
399C4×C41—22no—
400C4×C41—22no—
401C4×C41—41no—
402C4×C41—42no—
403C4×C41—41no—
404C4×C41—41no—
405C4×C41—81no—
406C4×C41—81no—
407C4×C41—81no—
408C4×C41C2×#12111yescharacteristic
409C4×C41#53811yescharacteristic
410C4×C41#54611yescharacteristic
411C4×C41#54611yescharacteristic
412C2×#460C2×C4111yescharacteristic, complemented
413C2×#449C2×C4111yescharacteristic, complemented
414C2×#449C2×C4111yescharacteristic, complemented
415C2×C4×SD16C2×C4111yescharacteristic, complemented
416#2428C2×C4111yescharacteristic, complemented
417#2341C2×C4111yescharacteristic, complemented
418#2065C2×C4111yescharacteristic, complemented
419#2034C2×C4111yescharacteristic, complemented
420#2033C2×C4111yescharacteristic, complemented
421#2011C2×C4111yescharacteristic, complemented
422#1970C2×C4111yescharacteristic, complemented
423#1923C2×C4111yescharacteristic, complemented
424#1880C2×C4111yescharacteristic, complemented
425#1879C2×C4111yescharacteristic, complemented
426#1863C2×C4111yescharacteristic, complemented
427C2×C41—81no—
428C2×C41—82no—
429C2×C41—82no—
430C2×C41—161no—
431C2×C41#242411yescharacteristic
432C2×C41#310611yescharacteristic
433C2×C41#311911yescharacteristic
434C2×C41#326511yescharacteristic
435C2×C41#327411yescharacteristic
436C2×C41#328211yescharacteristic
437C2×C41#328711yescharacteristic
438C22×#41C22×C4111yescharacteristic
439C22×SD16C22×C4111yescharacteristic
440C22×SD16C22×C4111yescharacteristic
441C22×D8C22×C4111yescharacteristic
442C22×D8C22×C4111yescharacteristic
443C2×#127C22×C4111yescharacteristic
444C2×#121—21no—
445C2×#121C22×C4111yescharacteristic
446C2×#121C22×C4111yescharacteristic
447C2×C4×Q8C22×C4111yescharacteristic
448C2×C4×Q8C22×C4111yescharacteristic
449C2×C4×D4C22×C4111yescharacteristic
450#460—24no—
451#449—24no—
452#449—24no—
453C4×SD16—24no—
454C2×#107C22×C4111yescharacteristic
455C2×#106C22×C4111yescharacteristic
456C2×C4⋊C8C22×C4111yescharacteristic
457C2×#103C22×C4111yescharacteristic
458C2×#103C22×C4111yescharacteristic
459C2×#102C22×C4111yescharacteristic
460C2×#102C22×C4111yescharacteristic
461C2×#102C22×C4111yescharacteristic
462C2×#102C22×C4111yescharacteristic
463C2×#102C22×C4111yescharacteristic
464C2×#102C22×C4111yescharacteristic
465C2×C22⋊C8C22×C4111yescharacteristic
466C2×C22⋊C8C22×C4111yescharacteristic
467C2×C4×C8C22×C4111yescharacteristic
468#394—21no—
469#392—21no—
470#390—21no—
471#390—21no—
472#390C22×C4111yescharacteristic
473#390C22×C4111yescharacteristic
474#390C22×C4111yescharacteristic
475#389C22×C4111yescharacteristic
476#386—21no—
477#380—21no—
478#380C22×C4111yescharacteristic
479C4×C22⋊C4—21no—
480C4×C22⋊C4C22×C4111yescharacteristic
481#340C22×C4111yescharacteristic
482#340C22×C4111yescharacteristic
483#336C22×C4111yescharacteristic
484#336C22×C4111yescharacteristic
485C41#2515911yescharacteristic, direct product factor, Sylow
486C2×#41—22no—
487C2×#41—22no—
488C2×#41—22no—
489C2×#41—22no—
490C2×#41—41no—
491C2×#41—41no—
492C22×Q8C23×C4111yescharacteristic
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4C23×C4111yescharacteristic
499C22×D4C23×C4111yescharacteristic
500C22×D4C23×C4111yescharacteristic
501C23×C4—21no—
502C23×C4—21no—
503C23×C4C23×C4111yescharacteristic
504C2×SD16—22no—
505C2×SD16—22no—
506C2×SD16—22no—
507C2×SD16—22no—
508C2×SD16—22no—
509C2×SD16D4×C4114yescomplemented
510C2×D8—22no—
511C2×D8—22no—
512C2×D8—22no—
513C2×D8—22no—
514C2×D8—41no—
515C2×D8—41no—
516C22×C8C23×C4111yescharacteristic
517C22×C8C23×C4111yescharacteristic
518C22×C8C23×C4111yescharacteristic
519C22×C8C23×C4111yescharacteristic
520#127—22no—
521#127—41no—
522#121—22no—
523#121—22no—
524#121—44no—
525#121—41no—
526#121—41no—
527C4×Q8—22no—
528C4×Q8—22no—
529C4×Q8—41no—
530C4×Q8—41no—
531C4×D4—22no—
532C4×D4—41no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4C23×C4111yescharacteristic
537C2×C4⋊C4C23×C4111yescharacteristic
538C2×C4⋊C4C23×C4111yescharacteristic
539C2×C4⋊C4C23×C4111yescharacteristic
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4D4×C4111yescharacteristic
551C2×C22⋊C4D4×C4111yescharacteristic
552C2×C42—21no—
553C2×C42—21no—
554C2×C42C23×C4111yescharacteristic
555C2×C42C23×C4111yescharacteristic
556#107—41no—
557#106—22no—
558C4⋊C8—22no—
559#103—22no—
560#103D4×C4114yescomplemented
561#102—22no—
562#102—22no—
563#102—22no—
564#102—22no—
565#102—22no—
566#102—41no—
567C22⋊C8—22no—
568C22⋊C8—22no—
569C4×C8—22no—
570#95—21no—
571#95—21no—
572#95D4×C4111yescharacteristic
573#95D4×C4111yescharacteristic
574C24—21no—
575C24—21no—
576C24—21no—
577C24C2×D4×C4111yescharacteristic
578#41—44no—
579#41—44no—
580#41—44no—
581#41—44no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8C2×D4×C4112yes—
586C2×Q8C2×D4×C4112yes—
587C2×Q8#41×C4112yes—
588C2×D4—24no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—42no—
610C2×D4—42no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—42no—
615C2×D4—81no—
616C2×D4—81no—
617C2×D4—81no—
618C2×D4—81no—
619C2×D4C2×D4×C4112yes—
620C2×D4#41×C4112yes—
621C22×C4—21no—
622C22×C4—24no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—81no—
638C22×C4C2×D4×C4111yescharacteristic
639C22×C4C2×D4×C4111yescharacteristic
640C22×C4C2×D4×C4111yescharacteristic
641C22×C4C2×D4×C4111yescharacteristic
642C22×C4C2×D4×C4111yescharacteristic
643C22×C4C24×C4111yescharacteristic
644SD16—28no—
645SD16—44no—
646D8—44no—
647D8—44no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8C2×D4×C4112yes—
659C2×C8C2×D4×C4112yes—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—42no—
668C4⋊C4—42no—
669C4⋊C4—42no—
670C4⋊C4C2×D4×C4112yes—
671C22⋊C4—22no—
672C22⋊C4—22no—
673C22⋊C4—42no—
674C22⋊C4—42no—
675C22⋊C4—42no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—81no—
680C22⋊C4—81no—
681C22⋊C4—81no—
682C22⋊C4—81no—
683C42—21no—
684C42—21no—
685C42—21no—
686C42—21no—
687C42—42no—
688C42—42no—
689C23—21no—
690C23—22no—
691C23—22no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23C22×D4×C4111yescharacteristic
718Q8—22no—
719Q8—22no—
720Q8—22no—
721Q8#121×C4114yescomplemented
722D4—22no—
723D4—22no—
724D4—22no—
725D4—22no—
726D4—48no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—41no—
731D4—41no—
732D4—41no—
733D4—41no—
734D4—41no—
735D4—84no—
736D4—84no—
737D4—84no—
738D4—84no—
739C2×C4—22no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—22no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—48no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—84no—
773C2×C4#135×C4112yes—
774C2×C4AGL(1,ℤ/8)×C4112yes—
775C2×C4C22×D4×C4111yescharacteristic
776C2×C4C22×D4×C4111yescharacteristic
777C2×C4C2×#41×C4111yescharacteristic
778C2×C4C2×#41×C4111yescharacteristic
779C2×C4H(5,𝔽2)×C4111yescharacteristic
780C2×C4H(5,𝔽2)×C4111yescharacteristic
781C8—22no—
782C8—22no—
783C8—41no—
784C8—41no—
785C22—41no—
786C22—42no—
787C22—41no—
788C22—42no—
789C22—42no—
790C22—41no—
791C22—42no—
792C22—41no—
793C22—41no—
794C22—42no—
795C22—42no—
796C22—41no—
797C22—41no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22C41×#52511yescharacteristic
814C22D42×C4111yescharacteristic
815C22D42×C4111yescharacteristic
816C22C2×#135×C4111yescharacteristic
817C22C2×AGL(1,ℤ/8)×C4111yescharacteristic
818C22C41×#57611yescharacteristic
819C22C41×#57711yescharacteristic
820C4—24no—
821C4—22no—
822C4—22no—
823C4—41no—
824C4—42no—
825C4—41no—
826C4—41no—
827C4—81no—
828C4—81no—
829C4—81no—
830C4C2×#121×C4111yescharacteristic
831C4C41×#53811yescharacteristic
832C4C41×#54611yescharacteristic
833C4C41×#54611yescharacteristic
834C2—81no—
835C2—82no—
836C2—82no—
837C2—161no—
838C2C41×#242411yescharacteristic
839C2C41×#310611yescharacteristic
840C2C41×#311911yescharacteristic
841C2C41×#326511yescharacteristic
842C2C41×#327411yescharacteristic
843C2C41×#328211yescharacteristic
844C2C41×#328711yescharacteristic
subgroupG/H
center, socleC23×C41C22×D4
commutator, Frattini, cosocleC22×C4C24×C41
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
1. C2×C41×#460C2semidirect
2. C2×C41×#449C2semidirect
3. C2×C41×#449C2semidirect
4. C2×C4×SD16×C41C2semidirect
5. C41×#2428C2semidirect
6. C41×#2341C2semidirect
7. C41×#2065C2semidirect
8. C41×#2034C2semidirect
9. C41×#2033C2semidirect
10. C41×#2011C2semidirect
11. C41×#1970C2semidirect
12. C41×#1923C2semidirect
13. C41×#1880C2semidirect
14. C41×#1879C2semidirect
15. C41×#1863C2semidirect
86. C2×SD16×C41D4semidirect
137. #103×C41D4semidirect
298. Q8×C41#121semidirect
362. #25159C41direct (N × H)
412. C2×#460C2×C41semidirect
413. C2×#449C2×C41semidirect
414. C2×#449C2×C41semidirect
415. C2×C4×SD16C2×C41semidirect
416. #2428C2×C41semidirect
417. #2341C2×C41semidirect
418. #2065C2×C41semidirect
419. #2034C2×C41semidirect
420. #2033C2×C41semidirect
421. #2011C2×C41semidirect
422. #1970C2×C41semidirect
423. #1923C2×C41semidirect
424. #1880C2×C41semidirect
425. #1879C2×C41semidirect
426. #1863C2×C41semidirect
485. C41#25159direct (N × H)
509. C2×SD16D4×C41semidirect
560. #103D4×C41semidirect
721. Q8#121×C41semidirect

Maximal subgroups

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

subgroupindex
C2×C41×#4602
C2×C41×#4492
C2×C4×SD16×C412
C41×#24282
C41×#23412
C41×#20652
C41×#20342
C41×#20332
C41×#20112
C41×#19702
C41×#19232
C41×#18802
C41×#18792
C41×#18632
#2515941