Finite Group Databasebeta

← C41×#25401 #23801602

Subgroups — C41×#25401 #23801602

Order 10496.

1118 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#469C211yesmaximal, characteristic, complemented
2C2×C41×#465C211yesmaximal, characteristic, complemented
3C2×C41×#463C211yesmaximal, characteristic, complemented
4C2×C41×#435C211yesmaximal, characteristic, complemented
5C41×#2540C211yesmaximal, characteristic, complemented
6C41×#2537C211yesmaximal, characteristic, complemented
7C41×#2035C211yesmaximal, characteristic, complemented
8C41×#2034C211yesmaximal, characteristic, complemented
9C41×#2000C211yesmaximal, characteristic, complemented
10C41×#1999C211yesmaximal, characteristic, complemented
11C41×#1959C211yesmaximal, characteristic, complemented
12C41×#1948C211yesmaximal, characteristic, complemented
13C41×#1894C211yesmaximal, characteristic, complemented
14C41×#1893C211yesmaximal, characteristic, complemented
15C41×#1762C211yesmaximal, characteristic, complemented
16C22×SD16×C41C2211yescharacteristic
17C22×D8×C41C2211yescharacteristic
18C22×M16×C41C2211yescharacteristic
19C23×C8×C41C2211yescharacteristic
20C2×#124×C41C2211yescharacteristic
21C2×C22⋊Q8×C41C2211yescharacteristic
22C2×C22⋊Q8×C41C2211yescharacteristic
23C2×#121×C41—21no—
24C2×#121×C41C2211yescharacteristic
25C2×#121×C41C2211yescharacteristic
26C2×#121×C41C2211yescharacteristic
27C2×#121×C41C2211yescharacteristic
28C2×C4×D4×C41C2211yescharacteristic
29C2×C4×D4×C41C2211yescharacteristic
30C41×#469—24no—
31C41×#465—24no—
32C41×#463—24no—
33C41×#435—24no—
34C2×#106×C41C2211yescharacteristic
35C2×#106×C41C2211yescharacteristic
36C2×C4⋊C8×C41C2211yescharacteristic
37C2×#103×C41C2211yescharacteristic
38C2×#103×C41C2211yescharacteristic
39C2×#103×C41C2211yescharacteristic
40C2×#102×C41C2211yescharacteristic
41C2×#102×C41C2211yescharacteristic
42C2×#102×C41C2211yescharacteristic
43C2×#102×C41C2211yescharacteristic
44C2×#102×C41C2211yescharacteristic
45C2×C22⋊C8×C41C2211yescharacteristic
46C2×C22⋊C8×C41C2211yescharacteristic
47C2×#97×C41C2211yescharacteristic
48C41×#399—21no—
49C41×#394—21no—
50C41×#394—21no—
51C41×#392—21no—
52C41×#390—21no—
53C41×#390—21no—
54C41×#384C2211yescharacteristic
55C41×#380—21no—
56C41×#380C2211yescharacteristic
57C41×#380C2211yescharacteristic
58C4×C4⋊C4×C41C2211yescharacteristic
59C41×#340C2211yescharacteristic
60C41×#340C2211yescharacteristic
61C41×#340C2211yescharacteristic
62C41×#340C2211yescharacteristic
63C22×Q8×C41C2311yescharacteristic
64C22×D4×C41—21no—
65C22×D4×C41—21no—
66C22×D4×C41—21no—
67C22×D4×C41—21no—
68C22×D4×C41D411yescharacteristic
69C22×D4×C41C2311yescharacteristic
70C22×D4×C41C2311yescharacteristic
71C23×C4×C41—21no—
72C23×C4×C41C2311yescharacteristic
73C23×C4×C41C2311yescharacteristic
74C2×SD16×C41—22no—
75C2×SD16×C41—22no—
76C2×SD16×C41—41no—
77C2×D8×C41—22no—
78C2×D8×C41—22no—
79C2×D8×C41—41no—
80C2×M16×C41—22no—
81C2×M16×C41—22no—
82C2×M16×C41—41no—
83C22×C8×C41—22no—
84C22×C8×C41—22no—
85C22×C8×C41—41no—
86C22×C8×C41C2311yescharacteristic
87C22×C8×C41C2311yescharacteristic
88C22×C8×C41C2311yescharacteristic
89C22×C8×C41C2311yescharacteristic
90#124×C41—22no—
91#124×C41—22no—
92C22⋊Q8×C41—22no—
93C22⋊Q8×C41—22no—
94C22⋊Q8×C41—41no—
95C22⋊Q8×C41—41no—
96#121×C41—22no—
97#121×C41—22no—
98#121×C41—22no—
99#121×C41—22no—
100#121×C41—41no—
101#121×C41—41no—
102#121×C41—41no—
103#121×C41—41no—
104#121×C41—44no—
105C4×D4×C41—22no—
106C4×D4×C41—22no—
107C4×D4×C41—22no—
108C4×D4×C41—22no—
109C2×C4⋊C4×C41—21no—
110C2×C4⋊C4×C41—21no—
111C2×C4⋊C4×C41—21no—
112C2×C4⋊C4×C41—21no—
113C2×C4⋊C4×C41D411yescharacteristic
114C2×C4⋊C4×C41C2311yescharacteristic
115C2×C4⋊C4×C41C2311yescharacteristic
116C2×C4⋊C4×C41C2311yescharacteristic
117C2×C4⋊C4×C41C2311yescharacteristic
118C2×C4⋊C4×C41C2311yescharacteristic
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×C22⋊C4×C41D411yescharacteristic
131C2×C22⋊C4×C41D411yescharacteristic
132C2×C42×C41—21no—
133C2×C42×C41C2311yescharacteristic
134#106×C41—22no—
135#106×C41—22no—
136C4⋊C8×C41D414yescomplemented
137#103×C41—22no—
138#103×C41—22no—
139#103×C41—41no—
140#102×C41—22no—
141#102×C41—22no—
142#102×C41—22no—
143#102×C41—41no—
144#102×C41D414yescomplemented
145C22⋊C8×C41—22no—
146C22⋊C8×C41—22no—
147#97×C41—22no—
148#95×C41—21no—
149#95×C41—21no—
150#95×C41—21no—
151C24×C41—21no—
152C24×C41—21no—
153C24×C41C2×D411yescharacteristic
154C24×C41C2×D411yescharacteristic
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—22no—
162C2×D4×C41—22no—
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—41no—
175C2×D4×C41—42no—
176C2×D4×C41—42no—
177C2×D4×C41—42no—
178C2×D4×C41—42no—
179C2×D4×C41—42no—
180C2×D4×C41—42no—
181C2×D4×C41—42no—
182C2×D4×C41—42no—
183C2×D4×C41—81no—
184C2×D4×C41—81no—
185C2×D4×C41—81no—
186C2×D4×C41—81no—
187C2×D4×C41C2×D412yes—
188C22×C4×C41—21no—
189C22×C4×C41—21no—
190C22×C4×C41—21no—
191C22×C4×C41—21no—
192C22×C4×C41—21no—
193C22×C4×C41—21no—
194C22×C4×C41—21no—
195C22×C4×C41—21no—
196C22×C4×C41—21no—
197C22×C4×C41—21no—
198C22×C4×C41—21no—
199C22×C4×C41—21no—
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—42no—
207C22×C4×C41—42no—
208C22×C4×C41—42no—
209C22×C4×C41C2×D411yescharacteristic
210C22×C4×C41C2×D411yescharacteristic
211C22×C4×C41C2×D411yescharacteristic
212C22×C4×C41C2×D411yescharacteristic
213C22×C4×C41C2411yescharacteristic
214SD16×C41—44no—
215D8×C41—44no—
216M16×C41—44no—
217C2×C8×C41—21no—
218C2×C8×C41—21no—
219C2×C8×C41—21no—
220C2×C8×C41—21no—
221C2×C8×C41—21no—
222C2×C8×C41—21no—
223C2×C8×C41—21no—
224C2×C8×C41—21no—
225C2×C8×C41—21no—
226C2×C8×C41—44no—
227C2×C8×C41C2×D412yes—
228C2×C8×C41C2×D412yes—
229C2×C8×C41C2×D412yes—
230C4⋊C4×C41—22no—
231C4⋊C4×C41—21no—
232C4⋊C4×C41—21no—
233C4⋊C4×C41—21no—
234C4⋊C4×C41—21no—
235C4⋊C4×C41—21no—
236C4⋊C4×C41—21no—
237C4⋊C4×C41—21no—
238C4⋊C4×C41—21no—
239C4⋊C4×C41—42no—
240C4⋊C4×C41—42no—
241C4⋊C4×C41—42no—
242C4⋊C4×C41—81no—
243C4⋊C4×C41C2×D412yes—
244C4⋊C4×C41#4112yes—
245C22⋊C4×C41—22no—
246C22⋊C4×C41—22no—
247C22⋊C4×C41—42no—
248C22⋊C4×C41—42no—
249C22⋊C4×C41—42no—
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—42no—
257C22⋊C4×C41—42no—
258C42×C41—81no—
259C42×C41C2×D412yes—
260C42×C41#4112yes—
261C23×C41—21no—
262C23×C41—21no—
263C23×C41—21no—
264C23×C41—21no—
265C23×C41—21no—
266C23×C41—21no—
267C23×C41—21no—
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×C41AGL(1,ℤ/8)12yes—
289C23×C41C22×D411yescharacteristic
290Q8×C41—41no—
291Q8×C41—41no—
292Q8×C41—41no—
293Q8×C41—41no—
294D4×C41—22no—
295D4×C41—22no—
296D4×C41—44no—
297D4×C41—41no—
298D4×C41—41no—
299D4×C41—41no—
300D4×C41—41no—
301D4×C41—41no—
302D4×C41—41no—
303D4×C41—84no—
304D4×C41—84no—
305D4×C41—84no—
306D4×C41—84no—
307C2×C4×C41—21no—
308C2×C4×C41—21no—
309C2×C4×C41—21no—
310C2×C4×C41—21no—
311C2×C4×C41—21no—
312C2×C4×C41—21no—
313C2×C4×C41—21no—
314C2×C4×C41—22no—
315C2×C4×C41—21no—
316C2×C4×C41—22no—
317C2×C4×C41—21no—
318C2×C4×C41—21no—
319C2×C4×C41—41no—
320C2×C4×C41—41no—
321C2×C4×C41—41no—
322C2×C4×C41—41no—
323C2×C4×C41—41no—
324C2×C4×C41—41no—
325C2×C4×C41—41no—
326C2×C4×C41—41no—
327C2×C4×C41—41no—
328C2×C4×C41—41no—
329C2×C4×C41—41no—
330C2×C4×C41—41no—
331C2×C4×C41—41no—
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#12112yes—
345C2×C4×C41#12112yes—
346C2×C4×C41C22×D411yescharacteristic
347C2×C4×C41C22×D411yescharacteristic
348C2×C4×C41C2×#4111yescharacteristic
349C2×C4×C41C2×#4111yescharacteristic
350C2×C4×C41H(5,𝔽2)11yescharacteristic
351C2×C4×C41H(5,𝔽2)11yescharacteristic
352C8×C41—22no—
353C8×C41—22no—
354C8×C41—22no—
355C8×C41—41no—
356#25401C4111yesmaximal, characteristic, direct product factor, Sylow
357C22×C41—22no—
358C22×C41—22no—
359C22×C41—22no—
360C22×C41—41no—
361C22×C41—41no—
362C22×C41—41no—
363C22×C41—41no—
364C22×C41—41no—
365C22×C41—42no—
366C22×C41—41no—
367C22×C41—42no—
368C22×C41—41no—
369C22×C41—42no—
370C22×C41—41no—
371C22×C41—41no—
372C22×C41—41no—
373C22×C41—41no—
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×C41C2×#12111yescharacteristic
386C22×C41D4211yescharacteristic
387C22×C41#54611yescharacteristic
388C22×C41C2×AGL(1,ℤ/8)11yescharacteristic
389C22×C41#57511yescharacteristic
390C22×C41#57711yescharacteristic
391C22×C41#57711yescharacteristic
392C4×C41—22no—
393C4×C41—22no—
394C4×C41—41no—
395C4×C41—41no—
396C4×C41—42no—
397C4×C41—42no—
398C4×C41—81no—
399C4×C41—81no—
400C4×C41—81no—
401C4×C41—81no—
402C4×C41#53211yescharacteristic
403C4×C41#54011yescharacteristic
404C4×C41D4211yescharacteristic
405C4×C41#55011yescharacteristic
406C2×#469C2×C4111yescharacteristic, complemented
407C2×#465C2×C4111yescharacteristic, complemented
408C2×#463C2×C4111yescharacteristic, complemented
409C2×#435C2×C4111yescharacteristic, complemented
410#2540C2×C4111yescharacteristic, complemented
411#2537C2×C4111yescharacteristic, complemented
412#2035C2×C4111yescharacteristic, complemented
413#2034C2×C4111yescharacteristic, complemented
414#2000C2×C4111yescharacteristic, complemented
415#1999C2×C4111yescharacteristic, complemented
416#1959C2×C4111yescharacteristic, complemented
417#1948C2×C4111yescharacteristic, complemented
418#1894C2×C4111yescharacteristic, complemented
419#1893C2×C4111yescharacteristic, complemented
420#1762C2×C4111yescharacteristic, complemented
421C2×C41—42no—
422C2×C41—81no—
423C2×C41—82no—
424C2×C41—161no—
425C2×C41#242811yescharacteristic
426C2×C41#305511yescharacteristic
427C2×C41#306011yescharacteristic
428C2×C41#326511yescharacteristic
429C2×C41#326711yescharacteristic
430C2×C41#330611yescharacteristic
431C2×C41#332111yescharacteristic
432C22×SD16C22×C4111yescharacteristic
433C22×D8C22×C4111yescharacteristic
434C22×M16C22×C4111yescharacteristic
435C23×C8C22×C4111yescharacteristic
436C2×#124C22×C4111yescharacteristic
437C2×C22⋊Q8C22×C4111yescharacteristic
438C2×C22⋊Q8C22×C4111yescharacteristic
439C2×#121—21no—
440C2×#121C22×C4111yescharacteristic
441C2×#121C22×C4111yescharacteristic
442C2×#121C22×C4111yescharacteristic
443C2×#121C22×C4111yescharacteristic
444C2×C4×D4C22×C4111yescharacteristic
445C2×C4×D4C22×C4111yescharacteristic
446#469—24no—
447#465—24no—
448#463—24no—
449#435—24no—
450C2×#106C22×C4111yescharacteristic
451C2×#106C22×C4111yescharacteristic
452C2×C4⋊C8C22×C4111yescharacteristic
453C2×#103C22×C4111yescharacteristic
454C2×#103C22×C4111yescharacteristic
455C2×#103C22×C4111yescharacteristic
456C2×#102C22×C4111yescharacteristic
457C2×#102C22×C4111yescharacteristic
458C2×#102C22×C4111yescharacteristic
459C2×#102C22×C4111yescharacteristic
460C2×#102C22×C4111yescharacteristic
461C2×C22⋊C8C22×C4111yescharacteristic
462C2×C22⋊C8C22×C4111yescharacteristic
463C2×#97C22×C4111yescharacteristic
464#399—21no—
465#394—21no—
466#394—21no—
467#392—21no—
468#390—21no—
469#390—21no—
470#384C22×C4111yescharacteristic
471#380—21no—
472#380C22×C4111yescharacteristic
473#380C22×C4111yescharacteristic
474C4×C4⋊C4C22×C4111yescharacteristic
475#340C22×C4111yescharacteristic
476#340C22×C4111yescharacteristic
477#340C22×C4111yescharacteristic
478#340C22×C4111yescharacteristic
479C41#2540111yescharacteristic, direct product factor, Sylow
480C22×Q8C23×C4111yescharacteristic
481C22×D4—21no—
482C22×D4—21no—
483C22×D4—21no—
484C22×D4—21no—
485C22×D4D4×C4111yescharacteristic
486C22×D4C23×C4111yescharacteristic
487C22×D4C23×C4111yescharacteristic
488C23×C4—21no—
489C23×C4C23×C4111yescharacteristic
490C23×C4C23×C4111yescharacteristic
491C2×SD16—22no—
492C2×SD16—22no—
493C2×SD16—41no—
494C2×D8—22no—
495C2×D8—22no—
496C2×D8—41no—
497C2×M16—22no—
498C2×M16—22no—
499C2×M16—41no—
500C22×C8—22no—
501C22×C8—22no—
502C22×C8—41no—
503C22×C8C23×C4111yescharacteristic
504C22×C8C23×C4111yescharacteristic
505C22×C8C23×C4111yescharacteristic
506C22×C8C23×C4111yescharacteristic
507#124—22no—
508#124—22no—
509C22⋊Q8—22no—
510C22⋊Q8—22no—
511C22⋊Q8—41no—
512C22⋊Q8—41no—
513#121—22no—
514#121—22no—
515#121—22no—
516#121—22no—
517#121—41no—
518#121—41no—
519#121—41no—
520#121—41no—
521#121—44no—
522C4×D4—22no—
523C4×D4—22no—
524C4×D4—22no—
525C4×D4—22no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4D4×C4111yescharacteristic
531C2×C4⋊C4C23×C4111yescharacteristic
532C2×C4⋊C4C23×C4111yescharacteristic
533C2×C4⋊C4C23×C4111yescharacteristic
534C2×C4⋊C4C23×C4111yescharacteristic
535C2×C4⋊C4C23×C4111yescharacteristic
536C2×C22⋊C4—21no—
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⋊C4D4×C4111yescharacteristic
548C2×C22⋊C4D4×C4111yescharacteristic
549C2×C42—21no—
550C2×C42C23×C4111yescharacteristic
551#106—22no—
552#106—22no—
553C4⋊C8D4×C4114yescomplemented
554#103—22no—
555#103—22no—
556#103—41no—
557#102—22no—
558#102—22no—
559#102—22no—
560#102—41no—
561#102D4×C4114yescomplemented
562C22⋊C8—22no—
563C22⋊C8—22no—
564#97—22no—
565#95—21no—
566#95—21no—
567#95—21no—
568C24—21no—
569C24—21no—
570C24C2×D4×C4111yescharacteristic
571C24C2×D4×C4111yescharacteristic
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
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—41no—
592C2×D4—42no—
593C2×D4—42no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—81no—
601C2×D4—81no—
602C2×D4—81no—
603C2×D4—81no—
604C2×D4C2×D4×C4112yes—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4C2×D4×C4111yescharacteristic
627C22×C4C2×D4×C4111yescharacteristic
628C22×C4C2×D4×C4111yescharacteristic
629C22×C4C2×D4×C4111yescharacteristic
630C22×C4C24×C4111yescharacteristic
631SD16—44no—
632D8—44no—
633M16—44no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—44no—
644C2×C8C2×D4×C4112yes—
645C2×C8C2×D4×C4112yes—
646C2×C8C2×D4×C4112yes—
647C4⋊C4—22no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—42no—
657C4⋊C4—42no—
658C4⋊C4—42no—
659C4⋊C4—81no—
660C4⋊C4C2×D4×C4112yes—
661C4⋊C4#41×C4112yes—
662C22⋊C4—22no—
663C22⋊C4—22no—
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—42no—
673C22⋊C4—42no—
674C22⋊C4—42no—
675C42—81no—
676C42C2×D4×C4112yes—
677C42#41×C4112yes—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—22no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
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—
705C23AGL(1,ℤ/8)×C4112yes—
706C23C22×D4×C4111yescharacteristic
707Q8—41no—
708Q8—41no—
709Q8—41no—
710Q8—41no—
711D4—22no—
712D4—22no—
713D4—44no—
714D4—41no—
715D4—41no—
716D4—41no—
717D4—41no—
718D4—41no—
719D4—41no—
720D4—84no—
721D4—84no—
722D4—84no—
723D4—84no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—22no—
732C2×C4—21no—
733C2×C4—22no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
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—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—84no—
761C2×C4#121×C4112yes—
762C2×C4#121×C4112yes—
763C2×C4C22×D4×C4111yescharacteristic
764C2×C4C22×D4×C4111yescharacteristic
765C2×C4C2×#41×C4111yescharacteristic
766C2×C4C2×#41×C4111yescharacteristic
767C2×C4H(5,𝔽2)×C4111yescharacteristic
768C2×C4H(5,𝔽2)×C4111yescharacteristic
769C8—22no—
770C8—22no—
771C8—22no—
772C8—41no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—42no—
786C22—41no—
787C22—42no—
788C22—41no—
789C22—42no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22C2×#121×C4111yescharacteristic
802C22D42×C4111yescharacteristic
803C22C41×#54611yescharacteristic
804C22C2×AGL(1,ℤ/8)×C4111yescharacteristic
805C22C41×#57511yescharacteristic
806C22C41×#57711yescharacteristic
807C22C41×#57711yescharacteristic
808C4—22no—
809C4—22no—
810C4—42no—
811C4—41no—
812C4—41no—
813C4—42no—
814C4—81no—
815C4—81no—
816C4—81no—
817C4—81no—
818C4C41×#53211yescharacteristic
819C4C41×#54011yescharacteristic
820C4D42×C4111yescharacteristic
821C4C41×#55011yescharacteristic
822C2—42no—
823C2—81no—
824C2—82no—
825C2—161no—
826C2C41×#242811yescharacteristic
827C2C41×#305511yescharacteristic
828C2C41×#306011yescharacteristic
829C2C41×#326511yescharacteristic
830C2C41×#326711yescharacteristic
831C2C41×#330611yescharacteristic
832C2C41×#332111yescharacteristic
subgroupG/H
center, socleC23×C41C22×D4
commutator, Frattini, cosocleC22×C4C24×C41
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C41 ◁ C2×C4×D4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C41×#469C2semidirect
2. C2×C41×#465C2semidirect
3. C2×C41×#463C2semidirect
4. C2×C41×#435C2semidirect
5. C41×#2540C2semidirect
6. C41×#2537C2semidirect
7. C41×#2035C2semidirect
8. C41×#2034C2semidirect
9. C41×#2000C2semidirect
10. C41×#1999C2semidirect
11. C41×#1959C2semidirect
12. C41×#1948C2semidirect
13. C41×#1894C2semidirect
14. C41×#1893C2semidirect
15. C41×#1762C2semidirect
136. C4⋊C8×C41D4semidirect
144. #102×C41D4semidirect
356. #25401C41direct (N × H)
406. C2×#469C2×C41semidirect
407. C2×#465C2×C41semidirect
408. C2×#463C2×C41semidirect
409. C2×#435C2×C41semidirect
410. #2540C2×C41semidirect
411. #2537C2×C41semidirect
412. #2035C2×C41semidirect
413. #2034C2×C41semidirect
414. #2000C2×C41semidirect
415. #1999C2×C41semidirect
416. #1959C2×C41semidirect
417. #1948C2×C41semidirect
418. #1894C2×C41semidirect
419. #1893C2×C41semidirect
420. #1762C2×C41semidirect
479. C41#25401direct (N × H)
553. C4⋊C8D4×C41semidirect
561. #102D4×C41semidirect

Maximal subgroups

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

subgroupindex
C2×C41×#4692
C2×C41×#4652
C2×C41×#4632
C2×C41×#4352
C41×#25402
C41×#25372
C41×#20352
C41×#20342
C41×#20002
C41×#19992
C41×#19592
C41×#19482
C41×#18942
C41×#18932
C41×#17622
#2540141