Finite Group Databasebeta

← C41×#25142 #23801343

Subgroups — C41×#25142 #23801343

Order 10496.

986 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#473C211yesmaximal, characteristic, complemented
2C41×#3056C211yesmaximal, characteristic
3C41×#3004C211yesmaximal, characteristic
4C2×C41×#451C211yesmaximal, characteristic, complemented
5C41×#2933C211yesmaximal, characteristic
6C22×#101×C41C211yesmaximal, characteristic, complemented
7C41×#2064C211yesmaximal, characteristic, complemented
8C41×#2052C211yesmaximal, characteristic, complemented
9C41×#2047C211yesmaximal, characteristic, complemented
10C41×#2020C211yesmaximal, characteristic, complemented
11C41×#1979C211yesmaximal, characteristic, complemented
12C41×#1930C211yesmaximal, characteristic, complemented
13C41×#1908C211yesmaximal, characteristic, complemented
14C41×#1901C211yesmaximal, characteristic, complemented
15C41×#1855C211yesmaximal, characteristic, complemented
16C23×Q8×C41C2211yescharacteristic
17C2×#137×C41C2211yescharacteristic
18C2×#137×C41C2211yescharacteristic
19C2×#137×C41C2211yescharacteristic
20C22×Q16×C41C2211yescharacteristic
21C22×Q16×C41C2211yescharacteristic
22C2×#131×C41C2211yescharacteristic
23C22×M16×C41C2211yescharacteristic
24C22×M16×C41C2211yescharacteristic
25C41×#525C2211yescharacteristic
26C2×C22⋊Q8×C41C2211yescharacteristic
27C41×#473—24no—
28C41×#470—21no—
29C41×#468—21no—
30C41×#467—21no—
31C41×#465—21no—
32C41×#451—21no—
33C41×#451—21no—
34C41×#451—21no—
35C41×#451—21no—
36C41×#451—21no—
37C41×#451—21no—
38C41×#448—21no—
39C41×#448—21no—
40C41×#436—21no—
41C41×#435—21no—
42C41×#435—21no—
43C8×D4×C41—21no—
44C2×#108×C41C2211yescharacteristic
45C2×#108×C41C2211yescharacteristic
46C41×#428C2211yescharacteristic
47C41×#424C2211yescharacteristic
48C41×#419C2211yescharacteristic
49C41×#419C2211yescharacteristic
50C41×#419C2211yescharacteristic
51C41×#417C2211yescharacteristic
52C2×#103×C41C2211yescharacteristic
53C2×#103×C41C2211yescharacteristic
54C2×#101×C41—24no—
55C2×#101×C41C2211yescharacteristic
56C2×#101×C41C2211yescharacteristic
57C2×#101×C41C2211yescharacteristic
58C2×#101×C41C2211yescharacteristic
59C2×#101×C41C2211yescharacteristic
60C2×#101×C41C2211yescharacteristic
61C41×#408C2211yescharacteristic
62C41×#407C2211yescharacteristic
63C2×C22⋊C8×C41C2211yescharacteristic
64C41×#405C2211yescharacteristic
65C41×#343C2211yescharacteristic
66C41×#343C2211yescharacteristic
67C41×#341C2211yescharacteristic
68C41×#341C2211yescharacteristic
69C2×#41×C41C2311yescharacteristic
70C22×Q8×C41—22no—
71C22×Q8×C41—22no—
72C22×Q8×C41—21no—
73C22×Q8×C41—21no—
74C22×Q8×C41—21no—
75C22×Q8×C41—21no—
76C22×Q8×C41—21no—
77C22×Q8×C41—41no—
78C22×Q8×C41—41no—
79C22×Q8×C41C2311yescharacteristic
80C22×Q8×C41C2311yescharacteristic
81C22×Q8×C41C2311yescharacteristic
82C23×C4×C41—21no—
83C23×C4×C41C2311yescharacteristic
84#137×C41—22no—
85#137×C41—22no—
86#137×C41—22no—
87#137×C41—41no—
88#137×C41—41no—
89#137×C41—41no—
90C2×Q16×C41—22no—
91C2×Q16×C41—21no—
92C2×Q16×C41—21no—
93C2×Q16×C41—21no—
94C2×Q16×C41—22no—
95C2×Q16×C41—21no—
96C2×Q16×C41—21no—
97C2×Q16×C41—21no—
98C2×Q16×C41—21no—
99C2×Q16×C41—41no—
100C2×Q16×C41—41no—
101C2×SD16×C41—21no—
102C2×SD16×C41—21no—
103C2×SD16×C41—21no—
104#131×C41—22no—
105#131×C41—41no—
106C2×M16×C41—21no—
107C2×M16×C41—21no—
108C2×M16×C41—21no—
109C2×M16×C41—22no—
110C2×M16×C41—22no—
111C2×M16×C41—41no—
112C2×M16×C41—41no—
113C2×M16×C41C2311yescharacteristic
114C2×M16×C41C2311yescharacteristic
115C2×M16×C41C2311yescharacteristic
116C2×M16×C41C2311yescharacteristic
117C2×M16×C41C2311yescharacteristic
118C2×M16×C41C2311yescharacteristic
119C22×C8×C41—21no—
120C22×C8×C41—21no—
121C22×C8×C41—21no—
122C22×C8×C41C2311yescharacteristic
123C22×C8×C41C2311yescharacteristic
124#123×C41—21no—
125C22⋊Q8×C41—21no—
126C22⋊Q8×C41—21no—
127C22⋊Q8×C41—21no—
128C22⋊Q8×C41—21no—
129C22⋊Q8×C41D411yescharacteristic
130C22⋊Q8×C41D411yescharacteristic
131#121×C41D411yescharacteristic
132#121×C41D411yescharacteristic
133#120×C41—21no—
134C4×D4×C41—21no—
135C4×D4×C41—21no—
136#117×C41C2311yescharacteristic
137C2×C4⋊C4×C41—21no—
138C2×C4⋊C4×C41C2311yescharacteristic
139C2×C22⋊C4×C41—21no—
140#108×C41—22no—
141#108×C41—41no—
142#107×C41—21no—
143#106×C41—21no—
144C4⋊C8×C41—21no—
145C4⋊C8×C41—21no—
146#103×C41—21no—
147#103×C41—21no—
148#103×C41—21no—
149#103×C41—21no—
150#103×C41—21no—
151#103×C41—21no—
152#103×C41—21no—
153#103×C41—21no—
154#103×C41—21no—
155#103×C41—21no—
156#103×C41—21no—
157#102×C41—21no—
158#101×C41—22no—
159#101×C41—22no—
160#101×C41—22no—
161#101×C41—22no—
162#101×C41—41no—
163#101×C41D414yescomplemented
164C22⋊C8×C41—21no—
165C22⋊C8×C41—21no—
166C22⋊C8×C41—21no—
167C22⋊C8×C41—21no—
168C22⋊C8×C41D411yescharacteristic
169C22⋊C8×C41D411yescharacteristic
170C22⋊C8×C41D411yescharacteristic
171C22⋊C8×C41D411yescharacteristic
172#97×C41—21no—
173C4×C8×C41—21no—
174C24×C41#4111yescharacteristic
175#41×C41—21no—
176#41×C41—21no—
177#41×C41—21no—
178#41×C41—21no—
179C2×Q8×C41—24no—
180C2×Q8×C41—21no—
181C2×Q8×C41—21no—
182C2×Q8×C41—21no—
183C2×Q8×C41—21no—
184C2×Q8×C41—21no—
185C2×Q8×C41—21no—
186C2×Q8×C41—21no—
187C2×Q8×C41—21no—
188C2×Q8×C41—21no—
189C2×Q8×C41—21no—
190C2×Q8×C41—21no—
191C2×Q8×C41—21no—
192C2×Q8×C41—21no—
193C2×Q8×C41—21no—
194C2×Q8×C41—21no—
195C2×Q8×C41—21no—
196C2×Q8×C41—42no—
197C2×Q8×C41—42no—
198C2×Q8×C41—42no—
199C2×Q8×C41—42no—
200C2×Q8×C41—42no—
201C2×Q8×C41—42no—
202C2×Q8×C41—42no—
203C2×Q8×C41—42no—
204C2×Q8×C41—42no—
205C2×Q8×C41—41no—
206C2×Q8×C41—41no—
207C2×Q8×C41C2×D412yes—
208C2×Q8×C41C2×D411yescharacteristic
209C2×Q8×C41#4112yes—
210C2×D4×C41—21no—
211C2×D4×C41—21no—
212C2×D4×C41—21no—
213C2×D4×C41C2×D411yescharacteristic
214C22×C4×C41—21no—
215C22×C4×C41—21no—
216C22×C4×C41—21no—
217C22×C4×C41—21no—
218C22×C4×C41—24no—
219C22×C4×C41—21no—
220C22×C4×C41—21no—
221C22×C4×C41—21no—
222C22×C4×C41—21no—
223C22×C4×C41—21no—
224C22×C4×C41—42no—
225C22×C4×C41—41no—
226C22×C4×C41—41no—
227C22×C4×C41C2×D411yescharacteristic
228C22×C4×C41C2×D411yescharacteristic
229C22×C4×C41C2×D411yescharacteristic
230C22×C4×C41C2×D411yescharacteristic
231C22×C4×C41#4111yescharacteristic
232C22×C4×C41C2411yescharacteristic
233Q16×C41—42no—
234Q16×C41—42no—
235Q16×C41—42no—
236Q16×C41—42no—
237Q16×C41—42no—
238Q16×C41—42no—
239Q16×C41—42no—
240SD16×C41—42no—
241SD16×C41—42no—
242SD16×C41—42no—
243M16×C41—21no—
244M16×C41—21no—
245M16×C41—21no—
246M16×C41—21no—
247M16×C41—21no—
248M16×C41—21no—
249M16×C41—21no—
250M16×C41—21no—
251M16×C41—21no—
252M16×C41—21no—
253M16×C41—42no—
254M16×C41—42no—
255M16×C41—42no—
256M16×C41C2×D412yes—
257M16×C41C2×D412yes—
258C2×C8×C41—21no—
259C2×C8×C41—21no—
260C2×C8×C41—21no—
261C2×C8×C41—21no—
262C2×C8×C41—21no—
263C2×C8×C41—21no—
264C2×C8×C41—21no—
265C2×C8×C41—21no—
266C2×C8×C41—21no—
267C2×C8×C41—21no—
268C2×C8×C41—42no—
269C2×C8×C41—42no—
270C2×C8×C41—42no—
271C2×C8×C41C2×D411yescharacteristic
272C2×C8×C41C2×D411yescharacteristic
273C2×C8×C41C2×D411yescharacteristic
274C2×C8×C41C2×D411yescharacteristic
275C4⋊C4×C41—21no—
276C4⋊C4×C41—21no—
277C4⋊C4×C41—21no—
278C4⋊C4×C41—21no—
279C4⋊C4×C41—41no—
280C4⋊C4×C41—41no—
281C4⋊C4×C41C2×D411yescharacteristic
282C4⋊C4×C41C2×D411yescharacteristic
283C22⋊C4×C41—21no—
284C22⋊C4×C41—21no—
285C22⋊C4×C41—21no—
286C22⋊C4×C41—21no—
287C22⋊C4×C41—21no—
288C22⋊C4×C41—41no—
289C22⋊C4×C41—41no—
290C42×C41—21no—
291C23×C41—21no—
292C23×C41—21no—
293C23×C41—22no—
294C23×C41—21no—
295C23×C41—41no—
296C23×C41#12111yescharacteristic
297C23×C41#12111yescharacteristic
298C23×C41C2×#4111yescharacteristic
299Q8×C41—22no—
300Q8×C41—21no—
301Q8×C41—22no—
302Q8×C41—22no—
303Q8×C41—22no—
304Q8×C41—21no—
305Q8×C41—44no—
306Q8×C41—44no—
307Q8×C41—41no—
308Q8×C41—41no—
309Q8×C41—41no—
310Q8×C41—41no—
311Q8×C41—41no—
312Q8×C41—41no—
313Q8×C41—41no—
314Q8×C41—41no—
315D4×C41—21no—
316D4×C41—21no—
317D4×C41—41no—
318D4×C41—41no—
319D4×C41—42no—
320D4×C41—81no—
321C2×C4×C41—21no—
322C2×C4×C41—21no—
323C2×C4×C41—21no—
324C2×C4×C41—21no—
325C2×C4×C41—21no—
326C2×C4×C41—21no—
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—21no—
334C2×C4×C41—22no—
335C2×C4×C41—22no—
336C2×C4×C41—44no—
337C2×C4×C41—44no—
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—81no—
349C2×C4×C41#12111yescharacteristic
350C2×C4×C41#12111yescharacteristic
351C2×C4×C41C22×D411yescharacteristic
352C2×C4×C41C22×D411yescharacteristic
353C2×C4×C41C22×D411yescharacteristic
354C2×C4×C41C2×#4111yescharacteristic
355C2×C4×C41H(5,𝔽2)11yescharacteristic
356C2×C4×C41H(5,𝔽2)11yescharacteristic
357C8×C41—21no—
358C8×C41—21no—
359C8×C41—22no—
360C8×C41—22no—
361C8×C41—21no—
362C8×C41—21no—
363C8×C41—41no—
364C8×C41—41no—
365C8×C41—41no—
366C8×C41—41no—
367#25142C4111yesmaximal, characteristic, direct product factor, Sylow
368C22×C41—21no—
369C22×C41—21no—
370C22×C41—21no—
371C22×C41—21no—
372C22×C41—21no—
373C22×C41—21no—
374C22×C41—21no—
375C22×C41—42no—
376C22×C41—42no—
377C22×C41—41no—
378C22×C41—41no—
379C22×C41—41no—
380C22×C41#47312yescomplemented
381C22×C41C2×#12111yescharacteristic
382C22×C41#52511yescharacteristic
383C22×C41#53811yescharacteristic
384C4×C41—21no—
385C4×C41—21no—
386C4×C41—42no—
387C4×C41—42no—
388C4×C41—41no—
389C4×C41—41no—
390C4×C41—41no—
391C4×C41—81no—
392C4×C41—81no—
393C4×C41D4211yescharacteristic
394C4×C41D4211yescharacteristic
395C4×C41#54611yescharacteristic
396C4×C41#54611yescharacteristic
397C2×#473C2×C4111yescharacteristic, complemented
398#3056C2×C4111yescharacteristic
399#3004C2×C4111yescharacteristic
400C2×#451C2×C4111yescharacteristic, complemented
401#2933C2×C4111yescharacteristic
402C22×#101C2×C4111yescharacteristic, complemented
403#2064C2×C4111yescharacteristic, complemented
404#2052C2×C4111yescharacteristic, complemented
405#2047C2×C4111yescharacteristic, complemented
406#2020C2×C4111yescharacteristic, complemented
407#1979C2×C4111yescharacteristic, complemented
408#1930C2×C4111yescharacteristic, complemented
409#1908C2×C4111yescharacteristic, complemented
410#1901C2×C4111yescharacteristic, complemented
411#1855C2×C4111yescharacteristic, complemented
412C2×C41—21no—
413C2×C41—21no—
414C2×C41—22no—
415C2×C41—41no—
416C2×C41—81no—
417C2×C41#242411yescharacteristic
418C2×C41C2×#47311yescharacteristic
419C2×C41#306911yescharacteristic
420C23×Q8C22×C4111yescharacteristic
421C2×#137C22×C4111yescharacteristic
422C2×#137C22×C4111yescharacteristic
423C2×#137C22×C4111yescharacteristic
424C22×Q16C22×C4111yescharacteristic
425C22×Q16C22×C4111yescharacteristic
426C2×#131C22×C4111yescharacteristic
427C22×M16C22×C4111yescharacteristic
428C22×M16C22×C4111yescharacteristic
429#525C22×C4111yescharacteristic
430C2×C22⋊Q8C22×C4111yescharacteristic
431#473—24no—
432#470—21no—
433#468—21no—
434#467—21no—
435#465—21no—
436#451—21no—
437#451—21no—
438#451—21no—
439#451—21no—
440#451—21no—
441#451—21no—
442#448—21no—
443#448—21no—
444#436—21no—
445#435—21no—
446#435—21no—
447C8×D4—21no—
448C2×#108C22×C4111yescharacteristic
449C2×#108C22×C4111yescharacteristic
450#428C22×C4111yescharacteristic
451#424C22×C4111yescharacteristic
452#419C22×C4111yescharacteristic
453#419C22×C4111yescharacteristic
454#419C22×C4111yescharacteristic
455#417C22×C4111yescharacteristic
456C2×#103C22×C4111yescharacteristic
457C2×#103C22×C4111yescharacteristic
458C2×#101—24no—
459C2×#101C22×C4111yescharacteristic
460C2×#101C22×C4111yescharacteristic
461C2×#101C22×C4111yescharacteristic
462C2×#101C22×C4111yescharacteristic
463C2×#101C22×C4111yescharacteristic
464C2×#101C22×C4111yescharacteristic
465#408C22×C4111yescharacteristic
466#407C22×C4111yescharacteristic
467C2×C22⋊C8C22×C4111yescharacteristic
468#405C22×C4111yescharacteristic
469#343C22×C4111yescharacteristic
470#343C22×C4111yescharacteristic
471#341C22×C4111yescharacteristic
472#341C22×C4111yescharacteristic
473C41#2514211yescharacteristic, direct product factor, Sylow
474C2×#41C23×C4111yescharacteristic
475C22×Q8—22no—
476C22×Q8—22no—
477C22×Q8—21no—
478C22×Q8—21no—
479C22×Q8—21no—
480C22×Q8—21no—
481C22×Q8—21no—
482C22×Q8—41no—
483C22×Q8—41no—
484C22×Q8C23×C4111yescharacteristic
485C22×Q8C23×C4111yescharacteristic
486C22×Q8C23×C4111yescharacteristic
487C23×C4—21no—
488C23×C4C23×C4111yescharacteristic
489#137—22no—
490#137—22no—
491#137—22no—
492#137—41no—
493#137—41no—
494#137—41no—
495C2×Q16—22no—
496C2×Q16—21no—
497C2×Q16—21no—
498C2×Q16—21no—
499C2×Q16—22no—
500C2×Q16—21no—
501C2×Q16—21no—
502C2×Q16—21no—
503C2×Q16—21no—
504C2×Q16—41no—
505C2×Q16—41no—
506C2×SD16—21no—
507C2×SD16—21no—
508C2×SD16—21no—
509#131—22no—
510#131—41no—
511C2×M16—21no—
512C2×M16—21no—
513C2×M16—21no—
514C2×M16—22no—
515C2×M16—22no—
516C2×M16—41no—
517C2×M16—41no—
518C2×M16C23×C4111yescharacteristic
519C2×M16C23×C4111yescharacteristic
520C2×M16C23×C4111yescharacteristic
521C2×M16C23×C4111yescharacteristic
522C2×M16C23×C4111yescharacteristic
523C2×M16C23×C4111yescharacteristic
524C22×C8—21no—
525C22×C8—21no—
526C22×C8—21no—
527C22×C8C23×C4111yescharacteristic
528C22×C8C23×C4111yescharacteristic
529#123—21no—
530C22⋊Q8—21no—
531C22⋊Q8—21no—
532C22⋊Q8—21no—
533C22⋊Q8—21no—
534C22⋊Q8D4×C4111yescharacteristic
535C22⋊Q8D4×C4111yescharacteristic
536#121D4×C4111yescharacteristic
537#121D4×C4111yescharacteristic
538#120—21no—
539C4×D4—21no—
540C4×D4—21no—
541#117C23×C4111yescharacteristic
542C2×C4⋊C4—21no—
543C2×C4⋊C4C23×C4111yescharacteristic
544C2×C22⋊C4—21no—
545#108—22no—
546#108—41no—
547#107—21no—
548#106—21no—
549C4⋊C8—21no—
550C4⋊C8—21no—
551#103—21no—
552#103—21no—
553#103—21no—
554#103—21no—
555#103—21no—
556#103—21no—
557#103—21no—
558#103—21no—
559#103—21no—
560#103—21no—
561#103—21no—
562#102—21no—
563#101—22no—
564#101—22no—
565#101—22no—
566#101—22no—
567#101—41no—
568#101D4×C4114yescomplemented
569C22⋊C8—21no—
570C22⋊C8—21no—
571C22⋊C8—21no—
572C22⋊C8—21no—
573C22⋊C8D4×C4111yescharacteristic
574C22⋊C8D4×C4111yescharacteristic
575C22⋊C8D4×C4111yescharacteristic
576C22⋊C8D4×C4111yescharacteristic
577#97—21no—
578C4×C8—21no—
579C24#41×C4111yescharacteristic
580#41—21no—
581#41—21no—
582#41—21no—
583#41—21no—
584C2×Q8—24no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8—42no—
602C2×Q8—42no—
603C2×Q8—42no—
604C2×Q8—42no—
605C2×Q8—42no—
606C2×Q8—42no—
607C2×Q8—42no—
608C2×Q8—42no—
609C2×Q8—42no—
610C2×Q8—41no—
611C2×Q8—41no—
612C2×Q8C2×D4×C4112yes—
613C2×Q8C2×D4×C4111yescharacteristic
614C2×Q8#41×C4112yes—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4C2×D4×C4111yescharacteristic
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—24no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—42no—
630C22×C4—41no—
631C22×C4—41no—
632C22×C4C2×D4×C4111yescharacteristic
633C22×C4C2×D4×C4111yescharacteristic
634C22×C4C2×D4×C4111yescharacteristic
635C22×C4C2×D4×C4111yescharacteristic
636C22×C4#41×C4111yescharacteristic
637C22×C4C24×C4111yescharacteristic
638Q16—42no—
639Q16—42no—
640Q16—42no—
641Q16—42no—
642Q16—42no—
643Q16—42no—
644Q16—42no—
645SD16—42no—
646SD16—42no—
647SD16—42no—
648M16—21no—
649M16—21no—
650M16—21no—
651M16—21no—
652M16—21no—
653M16—21no—
654M16—21no—
655M16—21no—
656M16—21no—
657M16—21no—
658M16—42no—
659M16—42no—
660M16—42no—
661M16C2×D4×C4112yes—
662M16C2×D4×C4112yes—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—42no—
674C2×C8—42no—
675C2×C8—42no—
676C2×C8C2×D4×C4111yescharacteristic
677C2×C8C2×D4×C4111yescharacteristic
678C2×C8C2×D4×C4111yescharacteristic
679C2×C8C2×D4×C4111yescharacteristic
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—41no—
685C4⋊C4—41no—
686C4⋊C4C2×D4×C4111yescharacteristic
687C4⋊C4C2×D4×C4111yescharacteristic
688C22⋊C4—21no—
689C22⋊C4—21no—
690C22⋊C4—21no—
691C22⋊C4—21no—
692C22⋊C4—21no—
693C22⋊C4—41no—
694C22⋊C4—41no—
695C42—21no—
696C23—21no—
697C23—21no—
698C23—22no—
699C23—21no—
700C23—41no—
701C23#121×C4111yescharacteristic
702C23#121×C4111yescharacteristic
703C23C2×#41×C4111yescharacteristic
704Q8—22no—
705Q8—21no—
706Q8—22no—
707Q8—22no—
708Q8—22no—
709Q8—21no—
710Q8—44no—
711Q8—44no—
712Q8—41no—
713Q8—41no—
714Q8—41no—
715Q8—41no—
716Q8—41no—
717Q8—41no—
718Q8—41no—
719Q8—41no—
720D4—21no—
721D4—21no—
722D4—41no—
723D4—41no—
724D4—42no—
725D4—81no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—44no—
742C2×C4—44no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—81no—
754C2×C4#121×C4111yescharacteristic
755C2×C4#121×C4111yescharacteristic
756C2×C4C22×D4×C4111yescharacteristic
757C2×C4C22×D4×C4111yescharacteristic
758C2×C4C22×D4×C4111yescharacteristic
759C2×C4C2×#41×C4111yescharacteristic
760C2×C4H(5,𝔽2)×C4111yescharacteristic
761C2×C4H(5,𝔽2)×C4111yescharacteristic
762C8—21no—
763C8—21no—
764C8—22no—
765C8—22no—
766C8—21no—
767C8—21no—
768C8—41no—
769C8—41no—
770C8—41no—
771C8—41no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—21no—
776C22—21no—
777C22—21no—
778C22—21no—
779C22—42no—
780C22—42no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22C41×#47312yescomplemented
785C22C2×#121×C4111yescharacteristic
786C22C41×#52511yescharacteristic
787C22C41×#53811yescharacteristic
788C4—21no—
789C4—21no—
790C4—41no—
791C4—41no—
792C4—42no—
793C4—42no—
794C4—41no—
795C4—81no—
796C4—81no—
797C4D42×C4111yescharacteristic
798C4D42×C4111yescharacteristic
799C4C41×#54611yescharacteristic
800C4C41×#54611yescharacteristic
801C2—21no—
802C2—21no—
803C2—22no—
804C2—41no—
805C2—81no—
806C2C41×#242411yescharacteristic
807C2C2×C41×#47311yescharacteristic
808C2C41×#306911yescharacteristic
subgroupG/H
center, socleC22×C41C2×#121
commutator, Frattini, cosocleC22×C4C24×C41
prime radicalC41×#525C22
LCSG ▷ C22×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×#473C2semidirect
4. C2×C41×#451C2semidirect
6. C22×#101×C41C2semidirect
7. C41×#2064C2semidirect
8. C41×#2052C2semidirect
9. C41×#2047C2semidirect
10. C41×#2020C2semidirect
11. C41×#1979C2semidirect
12. C41×#1930C2semidirect
13. C41×#1908C2semidirect
14. C41×#1901C2semidirect
15. C41×#1855C2semidirect
163. #101×C41D4semidirect
367. #25142C41direct (N × H)
380. C22×C41#473semidirect
397. C2×#473C2×C41semidirect
400. C2×#451C2×C41semidirect
402. C22×#101C2×C41semidirect
403. #2064C2×C41semidirect
404. #2052C2×C41semidirect
405. #2047C2×C41semidirect
406. #2020C2×C41semidirect
407. #1979C2×C41semidirect
408. #1930C2×C41semidirect
409. #1908C2×C41semidirect
410. #1901C2×C41semidirect
411. #1855C2×C41semidirect
473. C41#25142direct (N × H)
568. #101D4×C41semidirect
784. C22C41×#473semidirect

Maximal subgroups

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

subgroupindex
C2×C41×#4732
C41×#30562
C41×#30042
C2×C41×#4512
C41×#29332
C22×#101×C412
C41×#20642
C41×#20522
C41×#20472
C41×#20202
C41×#19792
C41×#19302
C41×#19082
C41×#19012
C41×#18552
#2514241