Finite Group Databasebeta

← C41×#18434 #23794635

Subgroups — C41×#18434 #23794635

Order 10496.

982 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3560C211yesmaximal, characteristic, complemented
2C41×#3213C211yesmaximal, characteristic, complemented
3C41×#3211C211yesmaximal, characteristic, complemented
4C41×#2662C211yesmaximal, characteristic, complemented
5C41×#1606C211yesmaximal, characteristic, complemented
6C41×#1604C211yesmaximal, characteristic, complemented
7C41×#1603C211yesmaximal, characteristic, complemented
8C41×#1601C211yesmaximal, characteristic, complemented
9C41×#1600C211yesmaximal, characteristic, complemented
10C41×#1598C211yesmaximal, characteristic, complemented
11C41×#1597C211yesmaximal, characteristic, complemented
12C41×#1595C211yesmaximal, characteristic, complemented
13C41×#1509C211yesmaximal, characteristic, complemented
14C41×#1502C211yesmaximal, characteristic, complemented
15C41×#1473C211yesmaximal, characteristic, complemented
16C41×#563—21no—
17C41×#560—21no—
18C41×#553—21no—
19C41×#553—21no—
20C41×#551—21no—
21C41×#547—21no—
22C41×#546—21no—
23C41×#546—21no—
24C41×#542—21no—
25C41×#539—21no—
26C41×#539C2211yescharacteristic
27C41×#538—21no—
28C41×#538—21no—
29C41×#538C2211yescharacteristic
30C41×#537C2211yescharacteristic
31C41×#534C2211yescharacteristic
32C41×#532C2211yescharacteristic
33C41×#529C2211yescharacteristic
34C2×#126×C41C2211yescharacteristic
35C2×#124×C41C2211yescharacteristic, complemented
36C41×#496—21no—
37C41×#495—21no—
38C41×#489—21no—
39C41×#488—21no—
40C41×#464—21no—
41C41×#463—21no—
42C41×#463—21no—
43C41×#463—21no—
44C41×#451C2211yescharacteristic, complemented
45C41×#450C2211yescharacteristic, complemented
46C41×#448C2211yescharacteristic
47C41×#448C2211yescharacteristic
48C41×#448C2211yescharacteristic, complemented
49C41×#447C2211yescharacteristic
50C41×#447C2211yescharacteristic
51C41×#447C2211yescharacteristic, complemented
52C41×#432C2211yescharacteristic, complemented
53C41×#431C2211yescharacteristic, complemented
54C41×#396—21no—
55C41×#395C2211yescharacteristic, complemented
56C41×#394—21no—
57C41×#394C2211yescharacteristic, complemented
58C41×#393C2211yescharacteristic
59C41×#392C2211yescharacteristic
60C41×#390—21no—
61C41×#388—21no—
62C4×C4⋊C4×C41C2211yescharacteristic, complemented
63C41×#328C2211yescharacteristic, complemented
64C41×#328C2211yescharacteristic, complemented
65C41×#327C2211yescharacteristic
66C41×#327C2211yescharacteristic
67C41×#327C2211yescharacteristic
68C41×#327C2211yescharacteristic
69C41×#327C2211yescharacteristic, complemented
70C41×#327C2211yescharacteristic, complemented
71C41×#324C2211yescharacteristic, complemented
72C41×#324C2211yescharacteristic, complemented
73C41×#323C2211yescharacteristic
74C41×#323C2211yescharacteristic
75C2×#41×C41—21no—
76C2×#41×C41—21no—
77C22×Q8×C41C2311yescharacteristic
78C22×D4×C41—21no—
79C22×D4×C41—21no—
80C22×D4×C41C2311yescharacteristic
81C2×Q16×C41—21no—
82C2×SD16×C41—21no—
83C2×SD16×C41—21no—
84C2×SD16×C41—21no—
85C2×SD16×C41—21no—
86C2×D8×C41—21no—
87C2×D8×C41—21no—
88C2×D8×C41—21no—
89C4⋊Q8×C41—21no—
90C4⋊Q8×C41D411yescharacteristic, complemented
91#127×C41D411yescharacteristic, complemented
92#126×C41—21no—
93#126×C41—21no—
94#126×C41—21no—
95#126×C41—21no—
96#126×C41—21no—
97#126×C41—21no—
98#126×C41—21no—
99#126×C41—21no—
100#126×C41—21no—
101#125×C41—21no—
102#125×C41—21no—
103#125×C41D411yescharacteristic, complemented
104#124×C41—21no—
105#124×C41—21no—
106#124×C41—21no—
107#124×C41—21no—
108#124×C41—21no—
109#124×C41—21no—
110#124×C41—21no—
111#124×C41—21no—
112#124×C41D411yescharacteristic, complemented
113#123×C41—21no—
114#123×C41—21no—
115#123×C41—21no—
116#123×C41—21no—
117#123×C41—21no—
118#123×C41—21no—
119#123×C41—21no—
120#123×C41—21no—
121#123×C41—21no—
122#123×C41—21no—
123#123×C41—21no—
124#123×C41—21no—
125C22⋊Q8×C41—21no—
126C22⋊Q8×C41—21no—
127C22⋊Q8×C41—21no—
128C22⋊Q8×C41—21no—
129C22⋊Q8×C41—21no—
130C22⋊Q8×C41—21no—
131C22⋊Q8×C41—21no—
132C22⋊Q8×C41C2311yescharacteristic
133#121×C41—21no—
134#121×C41—21no—
135#121×C41—21no—
136#121×C41—21no—
137#121×C41—21no—
138#121×C41—21no—
139#121×C41—21no—
140#121×C41—21no—
141#121×C41—21no—
142#121×C41—21no—
143#121×C41—21no—
144#121×C41—21no—
145#121×C41C2311yescharacteristic
146#121×C41C2311yescharacteristic
147#121×C41C2311yescharacteristic
148#120×C41—21no—
149#120×C41—21no—
150#120×C41—21no—
151#120×C41—21no—
152#120×C41—21no—
153C4×Q8×C41D411yescharacteristic, complemented
154C4×D4×C41—21no—
155C4×D4×C41—21no—
156C4×D4×C41—21no—
157C4×D4×C41—21no—
158C4×D4×C41—21no—
159C4×D4×C41—21no—
160C4×D4×C41—21no—
161C4×D4×C41—21no—
162C4×D4×C41D411yescharacteristic, complemented
163C4×D4×C41D411yescharacteristic, complemented
164C4×D4×C41D411yescharacteristic, complemented
165#117×C41—21no—
166#117×C41—21no—
167C2×C4⋊C4×C41—21no—
168C2×C4⋊C4×C41—21no—
169C2×C4⋊C4×C41—21no—
170C2×C4⋊C4×C41D411yescharacteristic
171C2×C4⋊C4×C41D411yescharacteristic
172C2×C4⋊C4×C41C2311yescharacteristic
173C2×C22⋊C4×C41—21no—
174C2×C22⋊C4×C41—21no—
175C2×C22⋊C4×C41—21no—
176C2×C22⋊C4×C41—21no—
177C2×C22⋊C4×C41—21no—
178C2×C22⋊C4×C41—21no—
179C2×C22⋊C4×C41—21no—
180C2×C22⋊C4×C41—21no—
181C2×C22⋊C4×C41D411yescharacteristic
182C2×C22⋊C4×C41D411yescharacteristic
183C2×C22⋊C4×C41C2311yescharacteristic
184C2×C42×C41—21no—
185C2×C42×C41C2311yescharacteristic
186C4⋊C8×C41—21no—
187C4⋊C8×C41—21no—
188#103×C41—21no—
189#103×C41—21no—
190#103×C41—21no—
191#103×C41—21no—
192#102×C41—21no—
193#102×C41—21no—
194#102×C41—21no—
195#102×C41—21no—
196C22⋊C8×C41C2311yescharacteristic
197C22⋊C8×C41C2311yescharacteristic
198C22⋊C8×C41C2311yescharacteristic
199C22⋊C8×C41C2311yescharacteristic
200#97×C41—21no—
201C4×C8×C41—21no—
202#95×C41—21no—
203#95×C41—21no—
204#95×C41C2311yescharacteristic
205#95×C41C2311yescharacteristic
206C24×C41—21no—
207C24×C41—21no—
208C24×C41C2×D411yescharacteristic
209#41×C41—81no—
210#41×C41—81no—
211#41×C41—81no—
212#41×C41—81no—
213C2×Q8×C41—21no—
214C2×Q8×C41—21no—
215C2×Q8×C41—21no—
216C2×Q8×C41—21no—
217C2×Q8×C41—81no—
218C2×Q8×C41C2×D411yescharacteristic
219C2×D4×C41—21no—
220C2×D4×C41—21no—
221C2×D4×C41—21no—
222C2×D4×C41—21no—
223C2×D4×C41—21no—
224C2×D4×C41—21no—
225C2×D4×C41—21no—
226C2×D4×C41—21no—
227C2×D4×C41—21no—
228C2×D4×C41—21no—
229C2×D4×C41—21no—
230C2×D4×C41—21no—
231C2×D4×C41—21no—
232C2×D4×C41—21no—
233C2×D4×C41—42no—
234C2×D4×C41—81no—
235C2×D4×C41—81no—
236C2×D4×C41—81no—
237C2×D4×C41—81no—
238C2×D4×C41—81no—
239C2×D4×C41C2×D411yescharacteristic
240C2×D4×C41C2×D411yescharacteristic
241C2×D4×C41C2×D411yescharacteristic
242C22×C4×C41—21no—
243C22×C4×C41—21no—
244C22×C4×C41—21no—
245C22×C4×C41—21no—
246C22×C4×C41—21no—
247C22×C4×C41—21no—
248C22×C4×C41—21no—
249C22×C4×C41—21no—
250C22×C4×C41—21no—
251C22×C4×C41—21no—
252C22×C4×C41—21no—
253C22×C4×C41C2×D411yescharacteristic
254C22×C4×C41C2×D411yescharacteristic
255C22×C4×C41C2×D411yescharacteristic
256C22×C4×C41C2×D411yescharacteristic
257C22×C4×C41C2×D411yescharacteristic
258C22×C4×C41C2411yescharacteristic
259Q16×C41—81no—
260SD16×C41—81no—
261SD16×C41—81no—
262SD16×C41—81no—
263SD16×C41—81no—
264D8×C41—81no—
265D8×C41—81no—
266D8×C41—81no—
267C2×C8×C41—21no—
268C2×C8×C41—21no—
269C2×C8×C41—21no—
270C2×C8×C41—21no—
271C4⋊C4×C41—21no—
272C4⋊C4×C41—21no—
273C4⋊C4×C41—21no—
274C4⋊C4×C41—21no—
275C4⋊C4×C41—21no—
276C4⋊C4×C41—21no—
277C4⋊C4×C41—21no—
278C4⋊C4×C41—21no—
279C4⋊C4×C41—21no—
280C4⋊C4×C41—21no—
281C4⋊C4×C41—21no—
282C4⋊C4×C41—21no—
283C4⋊C4×C41—21no—
284C4⋊C4×C41—21no—
285C4⋊C4×C41—21no—
286C4⋊C4×C41—21no—
287C4⋊C4×C41—21no—
288C4⋊C4×C41—42no—
289C4⋊C4×C41—81no—
290C4⋊C4×C41C2×D411yescharacteristic
291C4⋊C4×C41C2×D411yescharacteristic
292C4⋊C4×C41C2×D411yescharacteristic
293C4⋊C4×C41C2×D411yescharacteristic
294C22⋊C4×C41—21no—
295C22⋊C4×C41—21no—
296C22⋊C4×C41—21no—
297C22⋊C4×C41—21no—
298C22⋊C4×C41—21no—
299C22⋊C4×C41—21no—
300C22⋊C4×C41—21no—
301C22⋊C4×C41—21no—
302C22⋊C4×C41—21no—
303C22⋊C4×C41—21no—
304C22⋊C4×C41—21no—
305C22⋊C4×C41—21no—
306C22⋊C4×C41—21no—
307C22⋊C4×C41—21no—
308C22⋊C4×C41—21no—
309C22⋊C4×C41—21no—
310C22⋊C4×C41—21no—
311C22⋊C4×C41—21no—
312C22⋊C4×C41—21no—
313C22⋊C4×C41—21no—
314C22⋊C4×C41—21no—
315C22⋊C4×C41—21no—
316C22⋊C4×C41—21no—
317C22⋊C4×C41—21no—
318C22⋊C4×C41—21no—
319C22⋊C4×C41—42no—
320C22⋊C4×C41—41no—
321C22⋊C4×C41—41no—
322C22⋊C4×C41—41no—
323C22⋊C4×C41—41no—
324C22⋊C4×C41—81no—
325C22⋊C4×C41—81no—
326C22⋊C4×C41—81no—
327C42×C41—21no—
328C42×C41—21no—
329C42×C41—21no—
330C42×C41—81no—
331C42×C41C2×D411yescharacteristic
332C42×C41C2×D411yescharacteristic
333C42×C41C2×D411yescharacteristic
334C42×C41C2×D411yescharacteristic
335C23×C41—21no—
336C23×C41—21no—
337C23×C41—21no—
338C23×C41—21no—
339C23×C41—21no—
340C23×C41—21no—
341C23×C41—41no—
342C23×C41—41no—
343C23×C41—41no—
344C23×C41—41no—
345C23×C41—41no—
346C23×C41—41no—
347C23×C41—41no—
348C23×C41—41no—
349C23×C41—41no—
350C23×C41—81no—
351C23×C41—81no—
352C23×C41—81no—
353C23×C41C22×D411yescharacteristic
354Q8×C41—41no—
355Q8×C41—41no—
356Q8×C41—41no—
357Q8×C41—41no—
358Q8×C41—41no—
359Q8×C41—81no—
360Q8×C41—81no—
361D4×C41—41no—
362D4×C41—41no—
363D4×C41—41no—
364D4×C41—41no—
365D4×C41—41no—
366D4×C41—41no—
367D4×C41—41no—
368D4×C41—41no—
369D4×C41—41no—
370D4×C41—41no—
371D4×C41—41no—
372D4×C41—41no—
373D4×C41—41no—
374D4×C41—81no—
375D4×C41—81no—
376D4×C41—81no—
377D4×C41—81no—
378D4×C41—81no—
379D4×C41—81no—
380D4×C41—81no—
381D4×C41—81no—
382D4×C41—81no—
383D4×C41—84no—
384C2×C4×C41—21no—
385C2×C4×C41—21no—
386C2×C4×C41—22no—
387C2×C4×C41—21no—
388C2×C4×C41—21no—
389C2×C4×C41—21no—
390C2×C4×C41—21no—
391C2×C4×C41—21no—
392C2×C4×C41—21no—
393C2×C4×C41—21no—
394C2×C4×C41—21no—
395C2×C4×C41—21no—
396C2×C4×C41—21no—
397C2×C4×C41—41no—
398C2×C4×C41—41no—
399C2×C4×C41—41no—
400C2×C4×C41—41no—
401C2×C4×C41—41no—
402C2×C4×C41—41no—
403C2×C4×C41—41no—
404C2×C4×C41—41no—
405C2×C4×C41—41no—
406C2×C4×C41—41no—
407C2×C4×C41—41no—
408C2×C4×C41—41no—
409C2×C4×C41—81no—
410C2×C4×C41—81no—
411C2×C4×C41—81no—
412C2×C4×C41—81no—
413C2×C4×C41—81no—
414C2×C4×C41—81no—
415C2×C4×C41—81no—
416C2×C4×C41—81no—
417C2×C4×C41#12011yescharacteristic
418C2×C4×C41#12011yescharacteristic
419C2×C4×C41#12011yescharacteristic
420C2×C4×C41#12011yescharacteristic
421C2×C4×C41C22×D411yescharacteristic
422C2×C4×C41C22×D411yescharacteristic
423C8×C41—41no—
424C8×C41—41no—
425C8×C41—41no—
426C8×C41—41no—
427#18434C4111yesmaximal, characteristic, direct product factor, Sylow
428C22×C41—21no—
429C22×C41—21no—
430C22×C41—41no—
431C22×C41—41no—
432C22×C41—41no—
433C22×C41—41no—
434C22×C41—41no—
435C22×C41—41no—
436C22×C41—41no—
437C22×C41—41no—
438C22×C41—41no—
439C22×C41—41no—
440C22×C41—41no—
441C22×C41—41no—
442C22×C41—81no—
443C22×C41—81no—
444C22×C41—81no—
445C22×C41—81no—
446C22×C41—81no—
447C22×C41—81no—
448C22×C41—81no—
449C22×C41—81no—
450C22×C41—81no—
451C22×C41—162no—
452C22×C41C2×#12011yescharacteristic
453C22×C41#57611yescharacteristic
454C22×C41#57711yescharacteristic
455C4×C41—21no—
456C4×C41—21no—
457C4×C41—21no—
458C4×C41—21no—
459C4×C41—21no—
460C4×C41—21no—
461C4×C41—42no—
462C4×C41—41no—
463C4×C41—41no—
464C4×C41—41no—
465C4×C41—41no—
466C4×C41—41no—
467C4×C41—41no—
468C4×C41—41no—
469C4×C41—41no—
470C4×C41—81no—
471C4×C41—81no—
472#3560C2×C4111yescharacteristic, complemented
473#3213C2×C4111yescharacteristic, complemented
474#3211C2×C4111yescharacteristic, complemented
475#2662C2×C4111yescharacteristic, complemented
476#1606C2×C4111yescharacteristic, complemented
477#1604C2×C4111yescharacteristic, complemented
478#1603C2×C4111yescharacteristic, complemented
479#1601C2×C4111yescharacteristic, complemented
480#1600C2×C4111yescharacteristic, complemented
481#1598C2×C4111yescharacteristic, complemented
482#1597C2×C4111yescharacteristic, complemented
483#1595C2×C4111yescharacteristic, complemented
484#1509C2×C4111yescharacteristic, complemented
485#1502C2×C4111yescharacteristic, complemented
486#1473C2×C4111yescharacteristic, complemented
487C2×C41—21no—
488C2×C41—21no—
489C2×C41—81no—
490C2×C41—81no—
491C2×C41—81no—
492C2×C41—81no—
493C2×C41—161no—
494C2×C41#301211yescharacteristic
495C2×C41#301811yescharacteristic
496C2×C41#302711yescharacteristic
497#563—21no—
498#560—21no—
499#553—21no—
500#553—21no—
501#551—21no—
502#547—21no—
503#546—21no—
504#546—21no—
505#542—21no—
506#539—21no—
507#539C22×C4111yescharacteristic
508#538—21no—
509#538—21no—
510#538C22×C4111yescharacteristic
511#537C22×C4111yescharacteristic
512#534C22×C4111yescharacteristic
513#532C22×C4111yescharacteristic
514#529C22×C4111yescharacteristic
515C2×#126C22×C4111yescharacteristic
516C2×#124C22×C4111yescharacteristic, complemented
517#496—21no—
518#495—21no—
519#489—21no—
520#488—21no—
521#464—21no—
522#463—21no—
523#463—21no—
524#463—21no—
525#451C22×C4111yescharacteristic, complemented
526#450C22×C4111yescharacteristic, complemented
527#448C22×C4111yescharacteristic
528#448C22×C4111yescharacteristic
529#448C22×C4111yescharacteristic, complemented
530#447C22×C4111yescharacteristic
531#447C22×C4111yescharacteristic
532#447C22×C4111yescharacteristic, complemented
533#432C22×C4111yescharacteristic, complemented
534#431C22×C4111yescharacteristic, complemented
535#396—21no—
536#395C22×C4111yescharacteristic, complemented
537#394—21no—
538#394C22×C4111yescharacteristic, complemented
539#393C22×C4111yescharacteristic
540#392C22×C4111yescharacteristic
541#390—21no—
542#388—21no—
543C4×C4⋊C4C22×C4111yescharacteristic, complemented
544#328C22×C4111yescharacteristic, complemented
545#328C22×C4111yescharacteristic, complemented
546#327C22×C4111yescharacteristic
547#327C22×C4111yescharacteristic
548#327C22×C4111yescharacteristic
549#327C22×C4111yescharacteristic
550#327C22×C4111yescharacteristic, complemented
551#327C22×C4111yescharacteristic, complemented
552#324C22×C4111yescharacteristic, complemented
553#324C22×C4111yescharacteristic, complemented
554#323C22×C4111yescharacteristic
555#323C22×C4111yescharacteristic
556C41#1843411yescharacteristic, direct product factor, Sylow
557C2×#41—21no—
558C2×#41—21no—
559C22×Q8C23×C4111yescharacteristic
560C22×D4—21no—
561C22×D4—21no—
562C22×D4C23×C4111yescharacteristic
563C2×Q16—21no—
564C2×SD16—21no—
565C2×SD16—21no—
566C2×SD16—21no—
567C2×SD16—21no—
568C2×D8—21no—
569C2×D8—21no—
570C2×D8—21no—
571C4⋊Q8—21no—
572C4⋊Q8D4×C4111yescharacteristic, complemented
573#127D4×C4111yescharacteristic, complemented
574#126—21no—
575#126—21no—
576#126—21no—
577#126—21no—
578#126—21no—
579#126—21no—
580#126—21no—
581#126—21no—
582#126—21no—
583#125—21no—
584#125—21no—
585#125D4×C4111yescharacteristic, complemented
586#124—21no—
587#124—21no—
588#124—21no—
589#124—21no—
590#124—21no—
591#124—21no—
592#124—21no—
593#124—21no—
594#124D4×C4111yescharacteristic, complemented
595#123—21no—
596#123—21no—
597#123—21no—
598#123—21no—
599#123—21no—
600#123—21no—
601#123—21no—
602#123—21no—
603#123—21no—
604#123—21no—
605#123—21no—
606#123—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8—21no—
611C22⋊Q8—21no—
612C22⋊Q8—21no—
613C22⋊Q8—21no—
614C22⋊Q8C23×C4111yescharacteristic
615#121—21no—
616#121—21no—
617#121—21no—
618#121—21no—
619#121—21no—
620#121—21no—
621#121—21no—
622#121—21no—
623#121—21no—
624#121—21no—
625#121—21no—
626#121—21no—
627#121C23×C4111yescharacteristic
628#121C23×C4111yescharacteristic
629#121C23×C4111yescharacteristic
630#120—21no—
631#120—21no—
632#120—21no—
633#120—21no—
634#120—21no—
635C4×Q8D4×C4111yescharacteristic, complemented
636C4×D4—21no—
637C4×D4—21no—
638C4×D4—21no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—21no—
642C4×D4—21no—
643C4×D4—21no—
644C4×D4D4×C4111yescharacteristic, complemented
645C4×D4D4×C4111yescharacteristic, complemented
646C4×D4D4×C4111yescharacteristic, complemented
647#117—21no—
648#117—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4D4×C4111yescharacteristic
653C2×C4⋊C4D4×C4111yescharacteristic
654C2×C4⋊C4C23×C4111yescharacteristic
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4D4×C4111yescharacteristic
664C2×C22⋊C4D4×C4111yescharacteristic
665C2×C22⋊C4C23×C4111yescharacteristic
666C2×C42—21no—
667C2×C42C23×C4111yescharacteristic
668C4⋊C8—21no—
669C4⋊C8—21no—
670#103—21no—
671#103—21no—
672#103—21no—
673#103—21no—
674#102—21no—
675#102—21no—
676#102—21no—
677#102—21no—
678C22⋊C8C23×C4111yescharacteristic
679C22⋊C8C23×C4111yescharacteristic
680C22⋊C8C23×C4111yescharacteristic
681C22⋊C8C23×C4111yescharacteristic
682#97—21no—
683C4×C8—21no—
684#95—21no—
685#95—21no—
686#95C23×C4111yescharacteristic
687#95C23×C4111yescharacteristic
688C24—21no—
689C24—21no—
690C24C2×D4×C4111yescharacteristic
691#41—81no—
692#41—81no—
693#41—81no—
694#41—81no—
695C2×Q8—21no—
696C2×Q8—21no—
697C2×Q8—21no—
698C2×Q8—21no—
699C2×Q8—81no—
700C2×Q8C2×D4×C4111yescharacteristic
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—42no—
716C2×D4—81no—
717C2×D4—81no—
718C2×D4—81no—
719C2×D4—81no—
720C2×D4—81no—
721C2×D4C2×D4×C4111yescharacteristic
722C2×D4C2×D4×C4111yescharacteristic
723C2×D4C2×D4×C4111yescharacteristic
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4C2×D4×C4111yescharacteristic
736C22×C4C2×D4×C4111yescharacteristic
737C22×C4C2×D4×C4111yescharacteristic
738C22×C4C2×D4×C4111yescharacteristic
739C22×C4C2×D4×C4111yescharacteristic
740C22×C4C24×C4111yescharacteristic
741Q16—81no—
742SD16—81no—
743SD16—81no—
744SD16—81no—
745SD16—81no—
746D8—81no—
747D8—81no—
748D8—81no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—42no—
771C4⋊C4—81no—
772C4⋊C4C2×D4×C4111yescharacteristic
773C4⋊C4C2×D4×C4111yescharacteristic
774C4⋊C4C2×D4×C4111yescharacteristic
775C4⋊C4C2×D4×C4111yescharacteristic
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—21no—
800C22⋊C4—21no—
801C22⋊C4—42no—
802C22⋊C4—41no—
803C22⋊C4—41no—
804C22⋊C4—41no—
805C22⋊C4—41no—
806C22⋊C4—81no—
807C22⋊C4—81no—
808C22⋊C4—81no—
809C42—21no—
810C42—21no—
811C42—21no—
812C42—81no—
813C42C2×D4×C4111yescharacteristic
814C42C2×D4×C4111yescharacteristic
815C42C2×D4×C4111yescharacteristic
816C42C2×D4×C4111yescharacteristic
817C23—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—81no—
833C23—81no—
834C23—81no—
835C23C22×D4×C4111yescharacteristic
836Q8—41no—
837Q8—41no—
838Q8—41no—
839Q8—41no—
840Q8—41no—
841Q8—81no—
842Q8—81no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—41no—
849D4—41no—
850D4—41no—
851D4—41no—
852D4—41no—
853D4—41no—
854D4—41no—
855D4—41no—
856D4—81no—
857D4—81no—
858D4—81no—
859D4—81no—
860D4—81no—
861D4—81no—
862D4—81no—
863D4—81no—
864D4—81no—
865D4—84no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—22no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—81no—
892C2×C4—81no—
893C2×C4—81no—
894C2×C4—81no—
895C2×C4—81no—
896C2×C4—81no—
897C2×C4—81no—
898C2×C4—81no—
899C2×C4#120×C4111yescharacteristic
900C2×C4#120×C4111yescharacteristic
901C2×C4#120×C4111yescharacteristic
902C2×C4#120×C4111yescharacteristic
903C2×C4C22×D4×C4111yescharacteristic
904C2×C4C22×D4×C4111yescharacteristic
905C8—41no—
906C8—41no—
907C8—41no—
908C8—41no—
909C22—21no—
910C22—21no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—162no—
933C22C2×#120×C4111yescharacteristic
934C22C41×#57611yescharacteristic
935C22C41×#57711yescharacteristic
936C4—21no—
937C4—21no—
938C4—21no—
939C4—21no—
940C4—21no—
941C4—21no—
942C4—42no—
943C4—41no—
944C4—41no—
945C4—41no—
946C4—41no—
947C4—41no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—81no—
952C4—81no—
953C2—21no—
954C2—21no—
955C2—81no—
956C2—81no—
957C2—81no—
958C2—81no—
959C2—161no—
960C2C41×#301211yescharacteristic
961C2C41×#301811yescharacteristic
962C2C41×#302711yescharacteristic
subgroupG/H
center, socleC22×C41C2×#120
commutator, Frattini, cosocleC22×C4C24×C41
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C41 ◁ C2×C42×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C41×#3560C2semidirect
2. C41×#3213C2semidirect
3. C41×#3211C2semidirect
4. C41×#2662C2semidirect
5. C41×#1606C2semidirect
6. C41×#1604C2semidirect
7. C41×#1603C2semidirect
8. C41×#1601C2semidirect
9. C41×#1600C2semidirect
10. C41×#1598C2semidirect
11. C41×#1597C2semidirect
12. C41×#1595C2semidirect
13. C41×#1509C2semidirect
14. C41×#1502C2semidirect
15. C41×#1473C2semidirect
35. C2×#124×C41C22semidirect
44. C41×#451C22semidirect
45. C41×#450C22semidirect
48. C41×#448C22semidirect
51. C41×#447C22semidirect
52. C41×#432C22semidirect
53. C41×#431C22semidirect
55. C41×#395C22semidirect
57. C41×#394C22semidirect
62. C4×C4⋊C4×C41C22semidirect
63. C41×#328C22semidirect
64. C41×#328C22semidirect
69. C41×#327C22semidirect
70. C41×#327C22semidirect
71. C41×#324C22semidirect
72. C41×#324C22semidirect
90. C4⋊Q8×C41D4semidirect
91. #127×C41D4semidirect
103. #125×C41D4semidirect
112. #124×C41D4semidirect
153. C4×Q8×C41D4semidirect
162. C4×D4×C41D4semidirect
163. C4×D4×C41D4semidirect
164. C4×D4×C41D4semidirect
427. #18434C41direct (N × H)
472. #3560C2×C41semidirect
473. #3213C2×C41semidirect
474. #3211C2×C41semidirect
475. #2662C2×C41semidirect
476. #1606C2×C41semidirect
477. #1604C2×C41semidirect
478. #1603C2×C41semidirect
479. #1601C2×C41semidirect
480. #1600C2×C41semidirect
481. #1598C2×C41semidirect
482. #1597C2×C41semidirect
483. #1595C2×C41semidirect
484. #1509C2×C41semidirect
485. #1502C2×C41semidirect
486. #1473C2×C41semidirect
516. C2×#124C22×C41semidirect
525. #451C22×C41semidirect
526. #450C22×C41semidirect
529. #448C22×C41semidirect
532. #447C22×C41semidirect
533. #432C22×C41semidirect
534. #431C22×C41semidirect
536. #395C22×C41semidirect
538. #394C22×C41semidirect
543. C4×C4⋊C4C22×C41semidirect
544. #328C22×C41semidirect
545. #328C22×C41semidirect
550. #327C22×C41semidirect
551. #327C22×C41semidirect
552. #324C22×C41semidirect
553. #324C22×C41semidirect
556. C41#18434direct (N × H)
572. C4⋊Q8D4×C41semidirect
573. #127D4×C41semidirect
585. #125D4×C41semidirect
594. #124D4×C41semidirect
635. C4×Q8D4×C41semidirect
644. C4×D4D4×C41semidirect
645. C4×D4D4×C41semidirect
646. C4×D4D4×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#35602
C41×#32132
C41×#32112
C41×#26622
C41×#16062
C41×#16042
C41×#16032
C41×#16012
C41×#16002
C41×#15982
C41×#15972
C41×#15952
C41×#15092
C41×#15022
C41×#14732
#1843441