Finite Group Databasebeta

← C41×#33347 #23809548

Subgroups — C41×#33347 #23809548

Order 10496.

1236 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3449C211yesmaximal, characteristic
2C2×C41×#413C211yesmaximal, characteristic, complemented
3C2×C41×#410C211yesmaximal, characteristic, complemented
4C41×#2123C212yesmaximal, complemented
5C41×#2122C212yesmaximal, complemented
6C41×#2121C214yesmaximal, complemented
7C41×#2120C214yesmaximal, complemented
8C22×#41×C41C411yescharacteristic, complemented
9C22×#41×C41C2211yescharacteristic
10C22×M16×C41—21no—
11C41×#537—21no—
12C41×#537—21no—
13C41×#536—21no—
14C41×#536C411yescharacteristic, complemented
15C41×#536C2211yescharacteristic
16C41×#535—21no—
17C41×#535C411yescharacteristic, complemented
18C41×#535C2211yescharacteristic
19C41×#534C412yescomplemented
20C41×#534C2212yes—
21C41×#532—21no—
22C41×#532—21no—
23C41×#525—21no—
24C41×#525—21no—
25C41×#525C412yescomplemented
26C41×#525C2212yes—
27C2×#117×C41—21no—
28C2×#117×C41C411yescharacteristic, complemented
29C41×#413—21no—
30C41×#413—21no—
31C41×#413C2212yes—
32C41×#413C2212yes—
33C2×#101×C41—21no—
34C2×#100×C41C2212yes—
35C41×#410—21no—
36C41×#410—21no—
37C41×#410C2212yes—
38C41×#410C2212yes—
39C2×#99×C41—21no—
40C2×#99×C41C2212yes—
41C41×#352C2218yescomplemented
42C41×AΣL(1,𝔽16)C2218yescomplemented
43C2×#41×C41—21no—
44C2×#41×C41—21no—
45C2×#41×C41—21no—
46C2×#41×C41—21no—
47C2×#41×C41—41no—
48C2×#41×C41—41no—
49C2×#41×C41—41no—
50C2×#41×C41—41no—
51C2×#41×C41—41no—
52C2×#41×C41—41no—
53C2×#41×C41—41no—
54C2×#41×C41—41no—
55C2×#41×C41C2×C411yescharacteristic
56C2×#41×C41C2×C411yescharacteristic
57C2×#41×C41D411yescharacteristic
58C2×#41×C41D411yescharacteristic
59C2×#41×C41D411yescharacteristic
60C2×#41×C41D411yescharacteristic
61C2×#41×C41C2311yescharacteristic
62C2×#41×C41C2311yescharacteristic
63C22×Q8×C41C2×C411yescharacteristic, complemented
64C22×Q8×C41D411yescharacteristic
65C22×D4×C41C2×C411yescharacteristic
66C22×D4×C41C2×C412yes—
67C22×D4×C41C2×C411yescharacteristic, complemented
68C22×D4×C41D411yescharacteristic
69C22×D4×C41C2311yescharacteristic
70C23×C4×C41C2×C411yescharacteristic
71C23×C4×C41C2×C412yescomplemented
72C23×C4×C41D411yescharacteristic
73C23×C4×C41D411yescharacteristic
74C2×M16×C41—22no—
75C2×M16×C41—22no—
76C2×M16×C41—22no—
77C2×M16×C41—41no—
78C2×M16×C41—41no—
79C2×M16×C41—41no—
80C22×C8×C41—41no—
81C4⋊Q8×C41—21no—
82C4⋊Q8×C41—21no—
83#127×C41—21no—
84#127×C41—21no—
85#124×C41—21no—
86#124×C41—21no—
87#124×C41—21no—
88#124×C41—21no—
89#123×C41—22no—
90#123×C41—22no—
91#123×C41C2×C412yes—
92#123×C41C2×C412yescomplemented
93#123×C41C2×C412yescomplemented
94#123×C41C2312yes—
95C22⋊Q8×C41—22no—
96C22⋊Q8×C41—22no—
97C22⋊Q8×C41—21no—
98C22⋊Q8×C41—21no—
99C22⋊Q8×C41—21no—
100C22⋊Q8×C41—21no—
101#121×C41—22no—
102#121×C41—22no—
103#121×C41—22no—
104#121×C41—22no—
105#121×C41—22no—
106#121×C41—22no—
107#121×C41—21no—
108#121×C41—21no—
109#121×C41—21no—
110#121×C41—21no—
111#120×C41—22no—
112#120×C41—22no—
113#120×C41C2×C412yes—
114#120×C41C2×C412yescomplemented
115#120×C41C2×C412yescomplemented
116#120×C41C2312yes—
117C4×D4×C41—22no—
118C4×D4×C41—22no—
119C4×D4×C41—22no—
120C4×D4×C41—22no—
121#117×C41—21no—
122#117×C41—21no—
123#117×C41—22no—
124#117×C41—22no—
125#117×C41—41no—
126#117×C41—41no—
127#117×C41C2×C412yescomplemented
128#117×C41C2×C411yescharacteristic, complemented
129#117×C41C2×C411yescharacteristic, complemented
130C2×C4⋊C4×C41—21no—
131C2×C4⋊C4×C41—41no—
132C2×C22⋊C4×C41—22no—
133C2×C22⋊C4×C41C2×C412yes—
134C2×C42×C41—21no—
135C2×C42×C41—41no—
136#101×C41—22no—
137#101×C41—22no—
138#100×C41—22no—
139#100×C41C2314yes—
140#99×C41—22no—
141#99×C41—22no—
142#99×C41—22no—
143#99×C41C2314yes—
144C24×C41C22⋊C411yescharacteristic
145C24×C41C22×C411yescharacteristic
146C24×C41C22×C412yes—
147C24×C41C2×D411yescharacteristic
148#41×C41—41no—
149#41×C41—41no—
150#41×C41—41no—
151#41×C41—41no—
152#41×C41—41no—
153#41×C41—41no—
154#41×C41—41no—
155#41×C41—41no—
156#41×C41—41no—
157#41×C41—41no—
158#41×C41—41no—
159#41×C41—41no—
160#41×C41—41no—
161#41×C41—41no—
162#41×C41—41no—
163#41×C41—41no—
164#41×C41—42no—
165#41×C41—42no—
166#41×C41—42no—
167#41×C41—42no—
168#41×C41—42no—
169#41×C41—42no—
170#41×C41—41no—
171#41×C41—41no—
172#41×C41—41no—
173#41×C41—41no—
174C2×Q8×C41—21no—
175C2×Q8×C41—21no—
176C2×Q8×C41—41no—
177C2×Q8×C41—41no—
178C2×Q8×C41—41no—
179C2×Q8×C41—41no—
180C2×Q8×C41C22⋊C411yescharacteristic
181C2×Q8×C41C22⋊C411yescharacteristic
182C2×Q8×C41C2×D411yescharacteristic
183C2×Q8×C41C2×D411yescharacteristic
184C2×D4×C41—22no—
185C2×D4×C41—22no—
186C2×D4×C41—22no—
187C2×D4×C41—22no—
188C2×D4×C41—22no—
189C2×D4×C41—22no—
190C2×D4×C41—21no—
191C2×D4×C41—21no—
192C2×D4×C41—41no—
193C2×D4×C41—41no—
194C2×D4×C41—41no—
195C2×D4×C41—41no—
196C2×D4×C41—41no—
197C2×D4×C41—41no—
198C2×D4×C41—41no—
199C2×D4×C41—41no—
200C2×D4×C41—42no—
201C2×D4×C41—42no—
202C2×D4×C41C22⋊C411yescharacteristic
203C2×D4×C41C22⋊C411yescharacteristic
204C2×D4×C41C22⋊C411yescharacteristic
205C2×D4×C41C22⋊C411yescharacteristic
206C2×D4×C41C22×C411yescharacteristic
207C2×D4×C41C22×C411yescharacteristic
208C2×D4×C41C22×C411yescharacteristic
209C2×D4×C41C2×D411yescharacteristic
210C2×D4×C41C2×D411yescharacteristic
211C2×D4×C41C2×D411yescharacteristic
212C2×D4×C41C2×D411yescharacteristic
213C2×D4×C41C2411yescharacteristic
214C22×C4×C41—21no—
215C22×C4×C41—21no—
216C22×C4×C41—21no—
217C22×C4×C41—21no—
218C22×C4×C41—21no—
219C22×C4×C41—21no—
220C22×C4×C41—21no—
221C22×C4×C41—21no—
222C22×C4×C41—21no—
223C22×C4×C41—21no—
224C22×C4×C41—21no—
225C22×C4×C41—21no—
226C22×C4×C41—22no—
227C22×C4×C41—22no—
228C22×C4×C41—22no—
229C22×C4×C41—42no—
230C22×C4×C41—42no—
231C22×C4×C41—42no—
232C22×C4×C41C22⋊C411yescharacteristic
233C22×C4×C41C22⋊C411yescharacteristic
234C22×C4×C41C22⋊C411yescharacteristic
235C22×C4×C41C22⋊C411yescharacteristic
236C22×C4×C41C22⋊C411yescharacteristic
237C22×C4×C41C22⋊C411yescharacteristic
238C22×C4×C41C22⋊C411yescharacteristic
239C22×C4×C41C22⋊C411yescharacteristic
240C22×C4×C41C22⋊C411yescharacteristic
241C22×C4×C41C22×C411yescharacteristic
242C22×C4×C41C22×C411yescharacteristic
243C22×C4×C41C22×C412yes—
244C22×C4×C41C2×D411yescharacteristic
245C22×C4×C41C2×D411yescharacteristic
246C22×C4×C41C2×D411yescharacteristic
247C22×C4×C41C2×D411yescharacteristic
248C22×C4×C41C2×D411yescharacteristic
249M16×C41—24no—
250M16×C41—42no—
251M16×C41—42no—
252M16×C41—42no—
253C2×C8×C41—42no—
254C2×C8×C41—42no—
255C2×C8×C41—42no—
256C4⋊C4×C41—22no—
257C4⋊C4×C41—21no—
258C4⋊C4×C41—21no—
259C4⋊C4×C41—22no—
260C4⋊C4×C41—22no—
261C4⋊C4×C41—22no—
262C4⋊C4×C41—22no—
263C4⋊C4×C41—42no—
264C4⋊C4×C41—42no—
265C22⋊C4×C41—22no—
266C22⋊C4×C41—22no—
267C22⋊C4×C41—22no—
268C22⋊C4×C41—22no—
269C22⋊C4×C41—22no—
270C22⋊C4×C41—22no—
271C22⋊C4×C41—22no—
272C22⋊C4×C41—22no—
273C22⋊C4×C41—22no—
274C22⋊C4×C41—24no—
275C22⋊C4×C41—42no—
276C22⋊C4×C41C22×C412yes—
277C22⋊C4×C41C22×C412yes—
278C42×C41—22no—
279C42×C41—21no—
280C42×C41—21no—
281C42×C41—42no—
282C42×C41—42no—
283C23×C41—21no—
284C23×C41—21no—
285C23×C41—21no—
286C23×C41—21no—
287C23×C41—21no—
288C23×C41—21no—
289C23×C41—22no—
290C23×C41—42no—
291C23×C41—81no—
292C23×C41—81no—
293C23×C41—81no—
294C23×C41—82no—
295C23×C41C2×C22⋊C411yescharacteristic
296C23×C41C2×C22⋊C411yescharacteristic
297C23×C41C2×C22⋊C411yescharacteristic
298C23×C41C2×C22⋊C411yescharacteristic
299C23×C41C2×C22⋊C411yescharacteristic
300C23×C41C23×C411yescharacteristic
301C23×C41C22×D411yescharacteristic
302Q8×C41—41no—
303Q8×C41—41no—
304Q8×C41—41no—
305Q8×C41—41no—
306Q8×C41—42no—
307Q8×C41—41no—
308Q8×C41—41no—
309D4×C41—41no—
310D4×C41—41no—
311D4×C41—41no—
312D4×C41—41no—
313D4×C41—41no—
314D4×C41—41no—
315D4×C41—41no—
316D4×C41—41no—
317D4×C41—41no—
318D4×C41—41no—
319D4×C41—41no—
320D4×C41—41no—
321D4×C41—42no—
322D4×C41—44no—
323D4×C41—42no—
324D4×C41—42no—
325D4×C41—41no—
326D4×C41—41no—
327D4×C41—82no—
328D4×C41—82no—
329D4×C41—82no—
330D4×C41—82no—
331C2×C4×C41—21no—
332C2×C4×C41—21no—
333C2×C4×C41—21no—
334C2×C4×C41—21no—
335C2×C4×C41—21no—
336C2×C4×C41—21no—
337C2×C4×C41—21no—
338C2×C4×C41—21no—
339C2×C4×C41—21no—
340C2×C4×C41—21no—
341C2×C4×C41—21no—
342C2×C4×C41—21no—
343C2×C4×C41—21no—
344C2×C4×C41—21no—
345C2×C4×C41—21no—
346C2×C4×C41—21no—
347C2×C4×C41—21no—
348C2×C4×C41—21no—
349C2×C4×C41—21no—
350C2×C4×C41—21no—
351C2×C4×C41—21no—
352C2×C4×C41—21no—
353C2×C4×C41—21no—
354C2×C4×C41—21no—
355C2×C4×C41—21no—
356C2×C4×C41—21no—
357C2×C4×C41—21no—
358C2×C4×C41—21no—
359C2×C4×C41—21no—
360C2×C4×C41—21no—
361C2×C4×C41—22no—
362C2×C4×C41—22no—
363C2×C4×C41—22no—
364C2×C4×C41—44no—
365C2×C4×C41—42no—
366C2×C4×C41—42no—
367C2×C4×C41—42no—
368C2×C4×C41—44no—
369C2×C4×C41—82no—
370C2×C4×C41—84no—
371C2×C4×C41#9911yescharacteristic
372C2×C4×C41#9911yescharacteristic
373C2×C4×C41#9911yescharacteristic
374C2×C4×C41#9911yescharacteristic
375C2×C4×C41C2×C22⋊C411yescharacteristic
376C2×C4×C41C2×C22⋊C411yescharacteristic
377C2×C4×C41C2×C22⋊C411yescharacteristic
378C2×C4×C41C2×C22⋊C411yescharacteristic
379C2×C4×C41C2×C22⋊C411yescharacteristic
380C2×C4×C41C2×C22⋊C411yescharacteristic
381C2×C4×C41C2×C22⋊C411yescharacteristic
382C2×C4×C41C22×D411yescharacteristic
383C8×C41—44no—
384#33347C4111yesmaximal, characteristic, direct product factor, Sylow
385C22×C41—21no—
386C22×C41—21no—
387C22×C41—21no—
388C22×C41—21no—
389C22×C41—21no—
390C22×C41—21no—
391C22×C41—41no—
392C22×C41—41no—
393C22×C41—41no—
394C22×C41—41no—
395C22×C41—41no—
396C22×C41—41no—
397C22×C41—41no—
398C22×C41—42no—
399C22×C41—42no—
400C22×C41—42no—
401C22×C41—42no—
402C22×C41—42no—
403C22×C41—81no—
404C22×C41—81no—
405C22×C41—81no—
406C22×C41—81no—
407C22×C41—84no—
408C22×C41C2×#9911yescharacteristic
409C22×C41C2×#9911yescharacteristic
410C22×C41C22×C22⋊C411yescharacteristic
411C4×C41—21no—
412C4×C41—21no—
413C4×C41—21no—
414C4×C41—21no—
415C4×C41—21no—
416C4×C41—21no—
417C4×C41—42no—
418C4×C41—42no—
419C4×C41—42no—
420C4×C41—84no—
421C4×C41C2×#9911yescharacteristic
422C4×C41C2×#9911yescharacteristic
423C4×C41C2×#9911yescharacteristic
424C4×C41C2×#9911yescharacteristic
425#3449C2×C4111yescharacteristic
426C2×#413C2×C4111yescharacteristic, complemented
427C2×#410C2×C4111yescharacteristic, complemented
428#2123C2×C4112yescomplemented
429#2122C2×C4112yescomplemented
430#2121C2×C4114yescomplemented
431#2120C2×C4114yescomplemented
432C2×C41—21no—
433C2×C41—21no—
434C2×C41—21no—
435C2×C41—41no—
436C2×C41—41no—
437C2×C41—41no—
438C2×C41—41no—
439C2×C41—41no—
440C2×C41—41no—
441C2×C41—82no—
442C2×C41C22×#9911yescharacteristic
443C22×#41C4×C4111yescharacteristic, complemented
444C22×#41C22×C4111yescharacteristic
445C22×M16—21no—
446#537—21no—
447#537—21no—
448#536—21no—
449#536C4×C4111yescharacteristic, complemented
450#536C22×C4111yescharacteristic
451#535—21no—
452#535C4×C4111yescharacteristic, complemented
453#535C22×C4111yescharacteristic
454#534C4×C4112yescomplemented
455#534C22×C4112yes—
456#532—21no—
457#532—21no—
458#525—21no—
459#525—21no—
460#525C4×C4112yescomplemented
461#525C22×C4112yes—
462C2×#117—21no—
463C2×#117C4×C4111yescharacteristic, complemented
464#413—21no—
465#413—21no—
466#413C22×C4112yes—
467#413C22×C4112yes—
468C2×#101—21no—
469C2×#100C22×C4112yes—
470#410—21no—
471#410—21no—
472#410C22×C4112yes—
473#410C22×C4112yes—
474C2×#99—21no—
475C2×#99C22×C4112yes—
476#352C22×C4118yescomplemented
477AΣL(1,𝔽16)C22×C4118yescomplemented
478C41#3334711yescharacteristic, direct product factor, Sylow
479C2×#41—21no—
480C2×#41—21no—
481C2×#41—21no—
482C2×#41—21no—
483C2×#41—41no—
484C2×#41—41no—
485C2×#41—41no—
486C2×#41—41no—
487C2×#41—41no—
488C2×#41—41no—
489C2×#41—41no—
490C2×#41—41no—
491C2×#41C2×C4×C4111yescharacteristic
492C2×#41C2×C4×C4111yescharacteristic
493C2×#41D4×C4111yescharacteristic
494C2×#41D4×C4111yescharacteristic
495C2×#41D4×C4111yescharacteristic
496C2×#41D4×C4111yescharacteristic
497C2×#41C23×C4111yescharacteristic
498C2×#41C23×C4111yescharacteristic
499C22×Q8C2×C4×C4111yescharacteristic, complemented
500C22×Q8D4×C4111yescharacteristic
501C22×D4C2×C4×C4111yescharacteristic
502C22×D4C2×C4×C4112yes—
503C22×D4C2×C4×C4111yescharacteristic, complemented
504C22×D4D4×C4111yescharacteristic
505C22×D4C23×C4111yescharacteristic
506C23×C4C2×C4×C4111yescharacteristic
507C23×C4C2×C4×C4112yescomplemented
508C23×C4D4×C4111yescharacteristic
509C23×C4D4×C4111yescharacteristic
510C2×M16—22no—
511C2×M16—22no—
512C2×M16—22no—
513C2×M16—41no—
514C2×M16—41no—
515C2×M16—41no—
516C22×C8—41no—
517C4⋊Q8—21no—
518C4⋊Q8—21no—
519#127—21no—
520#127—21no—
521#124—21no—
522#124—21no—
523#124—21no—
524#124—21no—
525#123—22no—
526#123—22no—
527#123C2×C4×C4112yes—
528#123C2×C4×C4112yescomplemented
529#123C2×C4×C4112yescomplemented
530#123C23×C4112yes—
531C22⋊Q8—22no—
532C22⋊Q8—22no—
533C22⋊Q8—21no—
534C22⋊Q8—21no—
535C22⋊Q8—21no—
536C22⋊Q8—21no—
537#121—22no—
538#121—22no—
539#121—22no—
540#121—22no—
541#121—22no—
542#121—22no—
543#121—21no—
544#121—21no—
545#121—21no—
546#121—21no—
547#120—22no—
548#120—22no—
549#120C2×C4×C4112yes—
550#120C2×C4×C4112yescomplemented
551#120C2×C4×C4112yescomplemented
552#120C23×C4112yes—
553C4×D4—22no—
554C4×D4—22no—
555C4×D4—22no—
556C4×D4—22no—
557#117—21no—
558#117—21no—
559#117—22no—
560#117—22no—
561#117—41no—
562#117—41no—
563#117C2×C4×C4112yescomplemented
564#117C2×C4×C4111yescharacteristic, complemented
565#117C2×C4×C4111yescharacteristic, complemented
566C2×C4⋊C4—21no—
567C2×C4⋊C4—41no—
568C2×C22⋊C4—22no—
569C2×C22⋊C4C2×C4×C4112yes—
570C2×C42—21no—
571C2×C42—41no—
572#101—22no—
573#101—22no—
574#100—22no—
575#100C23×C4114yes—
576#99—22no—
577#99—22no—
578#99—22no—
579#99C23×C4114yes—
580C24C22⋊C4×C4111yescharacteristic
581C24C22×C4×C4111yescharacteristic
582C24C22×C4×C4112yes—
583C24C2×D4×C4111yescharacteristic
584#41—41no—
585#41—41no—
586#41—41no—
587#41—41no—
588#41—41no—
589#41—41no—
590#41—41no—
591#41—41no—
592#41—41no—
593#41—41no—
594#41—41no—
595#41—41no—
596#41—41no—
597#41—41no—
598#41—41no—
599#41—41no—
600#41—42no—
601#41—42no—
602#41—42no—
603#41—42no—
604#41—42no—
605#41—42no—
606#41—41no—
607#41—41no—
608#41—41no—
609#41—41no—
610C2×Q8—21no—
611C2×Q8—21no—
612C2×Q8—41no—
613C2×Q8—41no—
614C2×Q8—41no—
615C2×Q8—41no—
616C2×Q8C22⋊C4×C4111yescharacteristic
617C2×Q8C22⋊C4×C4111yescharacteristic
618C2×Q8C2×D4×C4111yescharacteristic
619C2×Q8C2×D4×C4111yescharacteristic
620C2×D4—22no—
621C2×D4—22no—
622C2×D4—22no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—22no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—41no—
629C2×D4—41no—
630C2×D4—41no—
631C2×D4—41no—
632C2×D4—41no—
633C2×D4—41no—
634C2×D4—41no—
635C2×D4—41no—
636C2×D4—42no—
637C2×D4—42no—
638C2×D4C22⋊C4×C4111yescharacteristic
639C2×D4C22⋊C4×C4111yescharacteristic
640C2×D4C22⋊C4×C4111yescharacteristic
641C2×D4C22⋊C4×C4111yescharacteristic
642C2×D4C22×C4×C4111yescharacteristic
643C2×D4C22×C4×C4111yescharacteristic
644C2×D4C22×C4×C4111yescharacteristic
645C2×D4C2×D4×C4111yescharacteristic
646C2×D4C2×D4×C4111yescharacteristic
647C2×D4C2×D4×C4111yescharacteristic
648C2×D4C2×D4×C4111yescharacteristic
649C2×D4C24×C4111yescharacteristic
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—42no—
668C22×C4C22⋊C4×C4111yescharacteristic
669C22×C4C22⋊C4×C4111yescharacteristic
670C22×C4C22⋊C4×C4111yescharacteristic
671C22×C4C22⋊C4×C4111yescharacteristic
672C22×C4C22⋊C4×C4111yescharacteristic
673C22×C4C22⋊C4×C4111yescharacteristic
674C22×C4C22⋊C4×C4111yescharacteristic
675C22×C4C22⋊C4×C4111yescharacteristic
676C22×C4C22⋊C4×C4111yescharacteristic
677C22×C4C22×C4×C4111yescharacteristic
678C22×C4C22×C4×C4111yescharacteristic
679C22×C4C22×C4×C4112yes—
680C22×C4C2×D4×C4111yescharacteristic
681C22×C4C2×D4×C4111yescharacteristic
682C22×C4C2×D4×C4111yescharacteristic
683C22×C4C2×D4×C4111yescharacteristic
684C22×C4C2×D4×C4111yescharacteristic
685M16—24no—
686M16—42no—
687M16—42no—
688M16—42no—
689C2×C8—42no—
690C2×C8—42no—
691C2×C8—42no—
692C4⋊C4—22no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—22no—
696C4⋊C4—22no—
697C4⋊C4—22no—
698C4⋊C4—22no—
699C4⋊C4—42no—
700C4⋊C4—42no—
701C22⋊C4—22no—
702C22⋊C4—22no—
703C22⋊C4—22no—
704C22⋊C4—22no—
705C22⋊C4—22no—
706C22⋊C4—22no—
707C22⋊C4—22no—
708C22⋊C4—22no—
709C22⋊C4—22no—
710C22⋊C4—24no—
711C22⋊C4—42no—
712C22⋊C4C22×C4×C4112yes—
713C22⋊C4C22×C4×C4112yes—
714C42—22no—
715C42—21no—
716C42—21no—
717C42—42no—
718C42—42no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—22no—
726C23—42no—
727C23—81no—
728C23—81no—
729C23—81no—
730C23—82no—
731C23C2×C22⋊C4×C4111yescharacteristic
732C23C2×C22⋊C4×C4111yescharacteristic
733C23C2×C22⋊C4×C4111yescharacteristic
734C23C2×C22⋊C4×C4111yescharacteristic
735C23C2×C22⋊C4×C4111yescharacteristic
736C23C23×C4×C4111yescharacteristic
737C23C22×D4×C4111yescharacteristic
738Q8—41no—
739Q8—41no—
740Q8—41no—
741Q8—41no—
742Q8—42no—
743Q8—41no—
744Q8—41no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—41no—
751D4—41no—
752D4—41no—
753D4—41no—
754D4—41no—
755D4—41no—
756D4—41no—
757D4—42no—
758D4—44no—
759D4—42no—
760D4—42no—
761D4—41no—
762D4—41no—
763D4—82no—
764D4—82no—
765D4—82no—
766D4—82no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—44no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—44no—
805C2×C4—82no—
806C2×C4—84no—
807C2×C4#99×C4111yescharacteristic
808C2×C4#99×C4111yescharacteristic
809C2×C4#99×C4111yescharacteristic
810C2×C4#99×C4111yescharacteristic
811C2×C4C2×C22⋊C4×C4111yescharacteristic
812C2×C4C2×C22⋊C4×C4111yescharacteristic
813C2×C4C2×C22⋊C4×C4111yescharacteristic
814C2×C4C2×C22⋊C4×C4111yescharacteristic
815C2×C4C2×C22⋊C4×C4111yescharacteristic
816C2×C4C2×C22⋊C4×C4111yescharacteristic
817C2×C4C2×C22⋊C4×C4111yescharacteristic
818C2×C4C22×D4×C4111yescharacteristic
819C8—44no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—81no—
839C22—81no—
840C22—81no—
841C22—81no—
842C22—84no—
843C22C2×#99×C4111yescharacteristic
844C22C2×#99×C4111yescharacteristic
845C22C22×C22⋊C4×C4111yescharacteristic
846C4—21no—
847C4—21no—
848C4—21no—
849C4—21no—
850C4—21no—
851C4—21no—
852C4—42no—
853C4—42no—
854C4—42no—
855C4—84no—
856C4C2×#99×C4111yescharacteristic
857C4C2×#99×C4111yescharacteristic
858C4C2×#99×C4111yescharacteristic
859C4C2×#99×C4111yescharacteristic
860C2—21no—
861C2—21no—
862C2—21no—
863C2—41no—
864C2—41no—
865C2—41no—
866C2—41no—
867C2—41no—
868C2—41no—
869C2—82no—
870C2C22×#99×C4111yescharacteristic
subgroupG/H
centerC4×C41C2×#99
commutatorC23C23×C4×C41
Frattini, cosocleC2×D4C24×C41
socleC2×C41C22×#99
prime radicalC41×#3449C2
LCSG ▷ C23 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C41 ◁ C22×C4×C41 ◁ C22×#41×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C41×#413C2semidirect
3. C2×C41×#410C2semidirect
4. C41×#2123C2semidirect
5. C41×#2122C2semidirect
6. C41×#2121C2semidirect
7. C41×#2120C2semidirect
8. C22×#41×C41C4semidirect
14. C41×#536C4semidirect
17. C41×#535C4semidirect
19. C41×#534C4semidirect
25. C41×#525C4semidirect
28. C2×#117×C41C4semidirect
41. C41×#352C22semidirect
42. C41×AΣL(1,𝔽16)C22semidirect
63. C22×Q8×C41C2×C4semidirect
67. C22×D4×C41C2×C4semidirect
71. C23×C4×C41C2×C4semidirect
92. #123×C41C2×C4semidirect
93. #123×C41C2×C4semidirect
114. #120×C41C2×C4semidirect
115. #120×C41C2×C4semidirect
127. #117×C41C2×C4semidirect
128. #117×C41C2×C4semidirect
129. #117×C41C2×C4semidirect
384. #33347C41direct (N × H)
426. C2×#413C2×C41semidirect
427. C2×#410C2×C41semidirect
428. #2123C2×C41semidirect
429. #2122C2×C41semidirect
430. #2121C2×C41semidirect
431. #2120C2×C41semidirect
443. C22×#41C4×C41semidirect
449. #536C4×C41semidirect
452. #535C4×C41semidirect
454. #534C4×C41semidirect
460. #525C4×C41semidirect
463. C2×#117C4×C41semidirect
476. #352C22×C41semidirect
477. AΣL(1,𝔽16)C22×C41semidirect
478. C41#33347direct (N × H)
499. C22×Q8C2×C4×C41semidirect
503. C22×D4C2×C4×C41semidirect
507. C23×C4C2×C4×C41semidirect
528. #123C2×C4×C41semidirect
529. #123C2×C4×C41semidirect
550. #120C2×C4×C41semidirect
551. #120C2×C4×C41semidirect
563. #117C2×C4×C41semidirect
564. #117C2×C4×C41semidirect
565. #117C2×C4×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#34492
C2×C41×#4132
C2×C41×#4102
C41×#21232
C41×#21222
C41×#21212
C41×#21202
#3334741