Finite Group Databasebeta

← C41×#25376 #23801577

Subgroups — C41×#25376 #23801577

Order 10496.

1162 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#496C211yesmaximal, characteristic, complemented
2C2×C41×#463C211yesmaximal, characteristic, complemented
3C2×C41×#459C211yesmaximal, characteristic, complemented
4C2×C41×#459C211yesmaximal, characteristic, complemented
5C41×#2544C211yesmaximal, characteristic, complemented
6C41×#2366C211yesmaximal, characteristic, complemented
7C41×#2055C211yesmaximal, characteristic, complemented
8C41×#2054C211yesmaximal, characteristic, complemented
9C41×#2012C211yesmaximal, characteristic, complemented
10C41×#2011C211yesmaximal, characteristic, complemented
11C41×#1983C211yesmaximal, characteristic, complemented
12C41×#1940C211yesmaximal, characteristic, complemented
13C41×#1879C211yesmaximal, characteristic, complemented
14C41×#1877C211yesmaximal, characteristic, complemented
15C41×#1762C211yesmaximal, characteristic, complemented
16C22×SD16×C41C2211yescharacteristic
17C22×SD16×C41C2211yescharacteristic
18C22×D8×C41C2211yescharacteristic
19C22×D8×C41C2211yescharacteristic
20C22×D8×C41C2211yescharacteristic
21C22×D8×C41C2211yescharacteristic
22C2×#127×C41C2211yescharacteristic
23C2×#127×C41C2211yescharacteristic
24C2×#124×C41C2211yescharacteristic
25C2×#124×C41C2211yescharacteristic
26C2×C4×D4×C41—21no—
27C2×C4×D4×C41C2211yescharacteristic
28C2×C4×D4×C41C2211yescharacteristic
29C2×C4×D4×C41C2211yescharacteristic
30C41×#496—24no—
31C41×#463—24no—
32C41×#459—24no—
33C41×#459—24no—
34C2×C4⋊C8×C41C2211yescharacteristic
35C2×C4⋊C8×C41C2211yescharacteristic
36C2×C4⋊C8×C41C2211yescharacteristic
37C2×#103×C41C2211yescharacteristic
38C2×#103×C41C2211yescharacteristic
39C2×#102×C41C2211yescharacteristic
40C2×#102×C41C2211yescharacteristic
41C2×#102×C41C2211yescharacteristic
42C2×#102×C41C2211yescharacteristic
43C2×#102×C41C2211yescharacteristic
44C2×#102×C41C2211yescharacteristic
45C2×#97×C41C2211yescharacteristic
46C41×#394—21no—
47C41×#394—21no—
48C41×#391C2211yescharacteristic
49C41×#390—21no—
50C41×#390C2211yescharacteristic
51C41×#390C2211yescharacteristic
52C41×#390C2211yescharacteristic
53C41×#386—21no—
54C41×#386—21no—
55C41×#386—21no—
56C41×#386—21no—
57C4×C4⋊C4×C41C2211yescharacteristic
58C4×C4⋊C4×C41C2211yescharacteristic
59C41×#340C2211yescharacteristic
60C41×#340C2211yescharacteristic
61C41×#336C2211yescharacteristic
62C41×#336C2211yescharacteristic
63C22×Q8×C41C2311yescharacteristic
64C22×D4×C41—21no—
65C22×D4×C41—21no—
66C22×D4×C41—21no—
67C22×D4×C41—21no—
68C22×D4×C41C2311yescharacteristic
69C22×D4×C41C2311yescharacteristic
70C22×D4×C41C2311yescharacteristic
71C22×D4×C41C2311yescharacteristic
72C23×C4×C41—21no—
73C23×C4×C41—21no—
74C23×C4×C41—21no—
75C2×SD16×C41—22no—
76C2×SD16×C41—22no—
77C2×SD16×C41—22no—
78C2×SD16×C41—22no—
79C2×SD16×C41—41no—
80C2×SD16×C41—41no—
81C2×D8×C41—22no—
82C2×D8×C41—22no—
83C2×D8×C41—22no—
84C2×D8×C41—22no—
85C2×D8×C41—22no—
86C2×D8×C41—22no—
87C2×D8×C41—22no—
88C2×D8×C41—22no—
89C2×D8×C41—41no—
90C2×D8×C41—41no—
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—22no—
99#127×C41—41no—
100#127×C41D414yescomplemented
101#124×C41—22no—
102#124×C41—22no—
103#124×C41—22no—
104#124×C41—41no—
105C4×D4×C41—22no—
106C4×D4×C41—22no—
107C4×D4×C41—22no—
108C4×D4×C41—22no—
109C4×D4×C41—41no—
110C4×D4×C41—41no—
111C4×D4×C41—44no—
112C2×C4⋊C4×C41D411yescharacteristic
113C2×C4⋊C4×C41D411yescharacteristic
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×C41—21no—
128C2×C22⋊C4×C41—21no—
129C2×C22⋊C4×C41—21no—
130C2×C42×C41—21no—
131C2×C42×C41C2311yescharacteristic
132C2×C42×C41C2311yescharacteristic
133C2×C42×C41C2311yescharacteristic
134C4⋊C8×C41—22no—
135C4⋊C8×C41—22no—
136C4⋊C8×C41—22no—
137#103×C41—22no—
138#103×C41—41no—
139#102×C41—22no—
140#102×C41—22no—
141#102×C41—22no—
142#102×C41—22no—
143#102×C41—41no—
144#102×C41D414yescomplemented
145#97×C41—22no—
146#95×C41—21no—
147#95×C41—21no—
148#95×C41—21no—
149#95×C41D411yescharacteristic
150#95×C41D411yescharacteristic
151C24×C41—21no—
152C24×C41—21no—
153C24×C41—21no—
154C24×C41—21no—
155C2×Q8×C41—21no—
156C2×Q8×C41—21no—
157C2×Q8×C41—21no—
158C2×Q8×C41—21no—
159C2×Q8×C41—21no—
160C2×Q8×C41—21no—
161C2×D4×C41—24no—
162C2×D4×C41—24no—
163C2×D4×C41—21no—
164C2×D4×C41—21no—
165C2×D4×C41—21no—
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—21no—
183C2×D4×C41—21no—
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—81no—
191C2×D4×C41—81no—
192C2×D4×C41—81no—
193C2×D4×C41—81no—
194C2×D4×C41C2×D412yes—
195C2×D4×C41C2×D412yes—
196C2×D4×C41C2×D412yes—
197C22×C4×C41—21no—
198C22×C4×C41—21no—
199C22×C4×C41—21no—
200C22×C4×C41—21no—
201C22×C4×C41—42no—
202C22×C4×C41—42no—
203C22×C4×C41—42no—
204C22×C4×C41—42no—
205C22×C4×C41—42no—
206C22×C4×C41—81no—
207C22×C4×C41—81no—
208C22×C4×C41—81no—
209C22×C4×C41—81no—
210C22×C4×C41C2×D411yescharacteristic
211C22×C4×C41C2×D411yescharacteristic
212C22×C4×C41C2×D411yescharacteristic
213C22×C4×C41C2×D411yescharacteristic
214C22×C4×C41C2×D411yescharacteristic
215C22×C4×C41C2×D411yescharacteristic
216C22×C4×C41C2411yescharacteristic
217SD16×C41—44no—
218SD16×C41—44no—
219D8×C41—44no—
220D8×C41—44no—
221D8×C41—44no—
222D8×C41—44no—
223C2×C8×C41—21no—
224C2×C8×C41—21no—
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×C41C2×D412yes—
234C2×C8×C41#4112yes—
235C4⋊C4×C41—22no—
236C4⋊C4×C41—21no—
237C4⋊C4×C41—21no—
238C4⋊C4×C41—21no—
239C4⋊C4×C41—21no—
240C4⋊C4×C41—21no—
241C4⋊C4×C41—41no—
242C4⋊C4×C41C2×D412yes—
243C22⋊C4×C41—42no—
244C22⋊C4×C41—42no—
245C22⋊C4×C41—42no—
246C22⋊C4×C41—42no—
247C22⋊C4×C41—42no—
248C22⋊C4×C41—42no—
249C22⋊C4×C41—42no—
250C22⋊C4×C41—42no—
251C22⋊C4×C41—42no—
252C22⋊C4×C41—81no—
253C22⋊C4×C41—81no—
254C22⋊C4×C41—81no—
255C22⋊C4×C41—81no—
256C42×C41—21no—
257C42×C41—21no—
258C42×C41—21no—
259C42×C41—21no—
260C42×C41—42no—
261C42×C41C2×D412yes—
262C42×C41#4112yes—
263C23×C41—22no—
264C23×C41—22no—
265C23×C41—22no—
266C23×C41—41no—
267C23×C41—41no—
268C23×C41—41no—
269C23×C41—41no—
270C23×C41—41no—
271C23×C41—41no—
272C23×C41—41no—
273C23×C41—41no—
274C23×C41—41no—
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×C41C22×D411yescharacteristic
292Q8×C41—41no—
293Q8×C41—41no—
294Q8×C41—41no—
295Q8×C41—41no—
296D4×C41—22no—
297D4×C41—22no—
298D4×C41—22no—
299D4×C41—22no—
300D4×C41—22no—
301D4×C41—22no—
302D4×C41—48no—
303D4×C41—41no—
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—41no—
313D4×C41—84no—
314D4×C41—84no—
315D4×C41—84no—
316C2×C4×C41—21no—
317C2×C4×C41—21no—
318C2×C4×C41—21no—
319C2×C4×C41—21no—
320C2×C4×C41—21no—
321C2×C4×C41—21no—
322C2×C4×C41—21no—
323C2×C4×C41—21no—
324C2×C4×C41—21no—
325C2×C4×C41—22no—
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—41no—
333C2×C4×C41—41no—
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—84no—
344C2×C4×C41—84no—
345C2×C4×C41—84no—
346C2×C4×C41#12112yes—
347C2×C4×C41#12112yes—
348C2×C4×C41AGL(1,ℤ/8)12yes—
349C2×C4×C41C22×D411yescharacteristic
350C2×C4×C41C22×D411yescharacteristic
351C2×C4×C41C2×#4111yescharacteristic
352C2×C4×C41C2×#4111yescharacteristic
353C2×C4×C41H(5,𝔽2)11yescharacteristic
354C2×C4×C41H(5,𝔽2)11yescharacteristic
355C8×C41—22no—
356C8×C41—22no—
357C8×C41—41no—
358C8×C41—41no—
359#25376C4111yesmaximal, characteristic, direct product factor, Sylow
360C22×C41—42no—
361C22×C41—42no—
362C22×C41—42no—
363C22×C41—42no—
364C22×C41—42no—
365C22×C41—42no—
366C22×C41—42no—
367C22×C41—42no—
368C22×C41—42no—
369C22×C41—81no—
370C22×C41—81no—
371C22×C41—81no—
372C22×C41—81no—
373C22×C41—81no—
374C22×C41—81no—
375C22×C41—81no—
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×C41C2×#12111yescharacteristic
389C22×C41D4211yescharacteristic
390C22×C41#55011yescharacteristic
391C22×C41C2×AGL(1,ℤ/8)11yescharacteristic
392C22×C41#57511yescharacteristic
393C22×C41#57611yescharacteristic
394C22×C41#57611yescharacteristic
395C4×C41—22no—
396C4×C41—22no—
397C4×C41—22no—
398C4×C41—41no—
399C4×C41—42no—
400C4×C41—41no—
401C4×C41—41no—
402C4×C41—81no—
403C4×C41—81no—
404C4×C41—81no—
405C4×C41#53211yescharacteristic
406C4×C41#54011yescharacteristic
407C4×C41D4211yescharacteristic
408C4×C41#54611yescharacteristic
409C2×#496C2×C4111yescharacteristic, complemented
410C2×#463C2×C4111yescharacteristic, complemented
411C2×#459C2×C4111yescharacteristic, complemented
412C2×#459C2×C4111yescharacteristic, complemented
413#2544C2×C4111yescharacteristic, complemented
414#2366C2×C4111yescharacteristic, complemented
415#2055C2×C4111yescharacteristic, complemented
416#2054C2×C4111yescharacteristic, complemented
417#2012C2×C4111yescharacteristic, complemented
418#2011C2×C4111yescharacteristic, complemented
419#1983C2×C4111yescharacteristic, complemented
420#1940C2×C4111yescharacteristic, complemented
421#1879C2×C4111yescharacteristic, complemented
422#1877C2×C4111yescharacteristic, complemented
423#1762C2×C4111yescharacteristic, complemented
424C2×C41—82no—
425C2×C41—82no—
426C2×C41—82no—
427C2×C41—161no—
428C2×C41#242811yescharacteristic
429C2×C41#303611yescharacteristic
430C2×C41#304111yescharacteristic
431C2×C41#326411yescharacteristic
432C2×C41#326811yescharacteristic
433C2×C41#339911yescharacteristic
434C2×C41#340311yescharacteristic
435C22×SD16C22×C4111yescharacteristic
436C22×SD16C22×C4111yescharacteristic
437C22×D8C22×C4111yescharacteristic
438C22×D8C22×C4111yescharacteristic
439C22×D8C22×C4111yescharacteristic
440C22×D8C22×C4111yescharacteristic
441C2×#127C22×C4111yescharacteristic
442C2×#127C22×C4111yescharacteristic
443C2×#124C22×C4111yescharacteristic
444C2×#124C22×C4111yescharacteristic
445C2×C4×D4—21no—
446C2×C4×D4C22×C4111yescharacteristic
447C2×C4×D4C22×C4111yescharacteristic
448C2×C4×D4C22×C4111yescharacteristic
449#496—24no—
450#463—24no—
451#459—24no—
452#459—24no—
453C2×C4⋊C8C22×C4111yescharacteristic
454C2×C4⋊C8C22×C4111yescharacteristic
455C2×C4⋊C8C22×C4111yescharacteristic
456C2×#103C22×C4111yescharacteristic
457C2×#103C22×C4111yescharacteristic
458C2×#102C22×C4111yescharacteristic
459C2×#102C22×C4111yescharacteristic
460C2×#102C22×C4111yescharacteristic
461C2×#102C22×C4111yescharacteristic
462C2×#102C22×C4111yescharacteristic
463C2×#102C22×C4111yescharacteristic
464C2×#97C22×C4111yescharacteristic
465#394—21no—
466#394—21no—
467#391C22×C4111yescharacteristic
468#390—21no—
469#390C22×C4111yescharacteristic
470#390C22×C4111yescharacteristic
471#390C22×C4111yescharacteristic
472#386—21no—
473#386—21no—
474#386—21no—
475#386—21no—
476C4×C4⋊C4C22×C4111yescharacteristic
477C4×C4⋊C4C22×C4111yescharacteristic
478#340C22×C4111yescharacteristic
479#340C22×C4111yescharacteristic
480#336C22×C4111yescharacteristic
481#336C22×C4111yescharacteristic
482C41#2537611yescharacteristic, direct product factor, Sylow
483C22×Q8C23×C4111yescharacteristic
484C22×D4—21no—
485C22×D4—21no—
486C22×D4—21no—
487C22×D4—21no—
488C22×D4C23×C4111yescharacteristic
489C22×D4C23×C4111yescharacteristic
490C22×D4C23×C4111yescharacteristic
491C22×D4C23×C4111yescharacteristic
492C23×C4—21no—
493C23×C4—21no—
494C23×C4—21no—
495C2×SD16—22no—
496C2×SD16—22no—
497C2×SD16—22no—
498C2×SD16—22no—
499C2×SD16—41no—
500C2×SD16—41no—
501C2×D8—22no—
502C2×D8—22no—
503C2×D8—22no—
504C2×D8—22no—
505C2×D8—22no—
506C2×D8—22no—
507C2×D8—22no—
508C2×D8—22no—
509C2×D8—41no—
510C2×D8—41no—
511C2×D8—41no—
512C2×D8—41no—
513C22×C8C23×C4111yescharacteristic
514C22×C8C23×C4111yescharacteristic
515C22×C8C23×C4111yescharacteristic
516C22×C8C23×C4111yescharacteristic
517#127—22no—
518#127—22no—
519#127—41no—
520#127D4×C4114yescomplemented
521#124—22no—
522#124—22no—
523#124—22no—
524#124—41no—
525C4×D4—22no—
526C4×D4—22no—
527C4×D4—22no—
528C4×D4—22no—
529C4×D4—41no—
530C4×D4—41no—
531C4×D4—44no—
532C2×C4⋊C4D4×C4111yescharacteristic
533C2×C4⋊C4D4×C4111yescharacteristic
534C2×C4⋊C4C23×C4111yescharacteristic
535C2×C4⋊C4C23×C4111yescharacteristic
536C2×C4⋊C4C23×C4111yescharacteristic
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
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×C42—21no—
551C2×C42C23×C4111yescharacteristic
552C2×C42C23×C4111yescharacteristic
553C2×C42C23×C4111yescharacteristic
554C4⋊C8—22no—
555C4⋊C8—22no—
556C4⋊C8—22no—
557#103—22no—
558#103—41no—
559#102—22no—
560#102—22no—
561#102—22no—
562#102—22no—
563#102—41no—
564#102D4×C4114yescomplemented
565#97—22no—
566#95—21no—
567#95—21no—
568#95—21no—
569#95D4×C4111yescharacteristic
570#95D4×C4111yescharacteristic
571C24—21no—
572C24—21no—
573C24—21no—
574C24—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×D4—24no—
582C2×D4—24no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
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—42no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—42no—
610C2×D4—81no—
611C2×D4—81no—
612C2×D4—81no—
613C2×D4—81no—
614C2×D4C2×D4×C4112yes—
615C2×D4C2×D4×C4112yes—
616C2×D4C2×D4×C4112yes—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—42no—
622C22×C4—42no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4—81no—
627C22×C4—81no—
628C22×C4—81no—
629C22×C4—81no—
630C22×C4C2×D4×C4111yescharacteristic
631C22×C4C2×D4×C4111yescharacteristic
632C22×C4C2×D4×C4111yescharacteristic
633C22×C4C2×D4×C4111yescharacteristic
634C22×C4C2×D4×C4111yescharacteristic
635C22×C4C2×D4×C4111yescharacteristic
636C22×C4C24×C4111yescharacteristic
637SD16—44no—
638SD16—44no—
639D8—44no—
640D8—44no—
641D8—44no—
642D8—44no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8C2×D4×C4112yes—
654C2×C8#41×C4112yes—
655C4⋊C4—22no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—41no—
662C4⋊C4C2×D4×C4112yes—
663C22⋊C4—42no—
664C22⋊C4—42no—
665C22⋊C4—42no—
666C22⋊C4—42no—
667C22⋊C4—42no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C22⋊C4—42no—
671C22⋊C4—42no—
672C22⋊C4—81no—
673C22⋊C4—81no—
674C22⋊C4—81no—
675C22⋊C4—81no—
676C42—21no—
677C42—21no—
678C42—21no—
679C42—21no—
680C42—42no—
681C42C2×D4×C4112yes—
682C42#41×C4112yes—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
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—
711C23C22×D4×C4111yescharacteristic
712Q8—41no—
713Q8—41no—
714Q8—41no—
715Q8—41no—
716D4—22no—
717D4—22no—
718D4—22no—
719D4—22no—
720D4—22no—
721D4—22no—
722D4—48no—
723D4—41no—
724D4—41no—
725D4—41no—
726D4—41no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—41no—
731D4—41no—
732D4—41no—
733D4—84no—
734D4—84no—
735D4—84no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—22no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—84no—
764C2×C4—84no—
765C2×C4—84no—
766C2×C4#121×C4112yes—
767C2×C4#121×C4112yes—
768C2×C4AGL(1,ℤ/8)×C4112yes—
769C2×C4C22×D4×C4111yescharacteristic
770C2×C4C22×D4×C4111yescharacteristic
771C2×C4C2×#41×C4111yescharacteristic
772C2×C4C2×#41×C4111yescharacteristic
773C2×C4H(5,𝔽2)×C4111yescharacteristic
774C2×C4H(5,𝔽2)×C4111yescharacteristic
775C8—22no—
776C8—22no—
777C8—41no—
778C8—41no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22C2×#121×C4111yescharacteristic
808C22D42×C4111yescharacteristic
809C22C41×#55011yescharacteristic
810C22C2×AGL(1,ℤ/8)×C4111yescharacteristic
811C22C41×#57511yescharacteristic
812C22C41×#57611yescharacteristic
813C22C41×#57611yescharacteristic
814C4—22no—
815C4—22no—
816C4—22no—
817C4—41no—
818C4—42no—
819C4—41no—
820C4—41no—
821C4—81no—
822C4—81no—
823C4—81no—
824C4C41×#53211yescharacteristic
825C4C41×#54011yescharacteristic
826C4D42×C4111yescharacteristic
827C4C41×#54611yescharacteristic
828C2—82no—
829C2—82no—
830C2—82no—
831C2—161no—
832C2C41×#242811yescharacteristic
833C2C41×#303611yescharacteristic
834C2C41×#304111yescharacteristic
835C2C41×#326411yescharacteristic
836C2C41×#326811yescharacteristic
837C2C41×#339911yescharacteristic
838C2C41×#340311yescharacteristic
subgroupG/H
center, socleC23×C41C22×D4
commutator, Frattini, cosocleC22×C4C24×C41
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C41 ◁ C4×C4⋊C4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C41×#496C2semidirect
2. C2×C41×#463C2semidirect
3. C2×C41×#459C2semidirect
4. C2×C41×#459C2semidirect
5. C41×#2544C2semidirect
6. C41×#2366C2semidirect
7. C41×#2055C2semidirect
8. C41×#2054C2semidirect
9. C41×#2012C2semidirect
10. C41×#2011C2semidirect
11. C41×#1983C2semidirect
12. C41×#1940C2semidirect
13. C41×#1879C2semidirect
14. C41×#1877C2semidirect
15. C41×#1762C2semidirect
100. #127×C41D4semidirect
144. #102×C41D4semidirect
359. #25376C41direct (N × H)
409. C2×#496C2×C41semidirect
410. C2×#463C2×C41semidirect
411. C2×#459C2×C41semidirect
412. C2×#459C2×C41semidirect
413. #2544C2×C41semidirect
414. #2366C2×C41semidirect
415. #2055C2×C41semidirect
416. #2054C2×C41semidirect
417. #2012C2×C41semidirect
418. #2011C2×C41semidirect
419. #1983C2×C41semidirect
420. #1940C2×C41semidirect
421. #1879C2×C41semidirect
422. #1877C2×C41semidirect
423. #1762C2×C41semidirect
482. C41#25376direct (N × H)
520. #127D4×C41semidirect
564. #102D4×C41semidirect

Maximal subgroups

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

subgroupindex
C2×C41×#4962
C2×C41×#4632
C2×C41×#4592
C41×#25442
C41×#23662
C41×#20552
C41×#20542
C41×#20122
C41×#20112
C41×#19832
C41×#19402
C41×#18792
C41×#18772
C41×#17622
#2537641