Finite Group Databasebeta

← C41×#25396 #23801597

Subgroups — C41×#25396 #23801597

Order 10496.

1184 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#469C211yesmaximal, characteristic, complemented
2C2×C41×#466C211yesmaximal, characteristic, complemented
3C2×C41×#459C211yesmaximal, characteristic, complemented
4C2×C41×#435C211yesmaximal, characteristic, complemented
5C41×#2541C211yesmaximal, characteristic, complemented
6C41×#2535C211yesmaximal, characteristic, complemented
7C41×#2034C211yesmaximal, characteristic, complemented
8C41×#2033C211yesmaximal, characteristic, complemented
9C41×#1999C211yesmaximal, characteristic, complemented
10C41×#1999C211yesmaximal, characteristic, complemented
11C41×#1961C211yesmaximal, characteristic, complemented
12C41×#1949C211yesmaximal, characteristic, complemented
13C41×#1895C211yesmaximal, characteristic, complemented
14C41×#1893C211yesmaximal, characteristic, complemented
15C41×#1762C211yesmaximal, characteristic, complemented
16C22×D8×C41C2211yescharacteristic
17C22×D8×C41C2211yescharacteristic
18C22×M16×C41C2211yescharacteristic
19C23×C8×C41C2211yescharacteristic
20C2×#127×C41—21no—
21C2×#127×C41C2211yescharacteristic
22C2×#121×C41C2211yescharacteristic
23C2×#121×C41C2211yescharacteristic
24C2×#121×C41C2211yescharacteristic
25C2×#121×C41C2211yescharacteristic
26C2×#121×C41C2211yescharacteristic
27C2×#121×C41C2211yescharacteristic
28C2×C4×D4×C41C2211yescharacteristic
29C2×C4×D4×C41C2211yescharacteristic
30C41×#469—24no—
31C41×#466—24no—
32C41×#459—24no—
33C41×#435—24no—
34C2×#107×C41C2211yescharacteristic
35C2×#106×C41C2211yescharacteristic
36C2×C4⋊C8×C41C2211yescharacteristic
37C2×#102×C41C2211yescharacteristic
38C2×#102×C41C2211yescharacteristic
39C2×#102×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×#397—21no—
49C41×#392—21no—
50C41×#392—21no—
51C41×#392—21no—
52C41×#390—21no—
53C41×#386—21no—
54C41×#386—21no—
55C41×#382C2211yescharacteristic
56C41×#380C2211yescharacteristic
57C41×#380C2211yescharacteristic
58C4×C4⋊C4×C41C2211yescharacteristic
59C41×#340C2211yescharacteristic
60C41×#340C2211yescharacteristic
61C41×#340C2211yescharacteristic
62C41×#340C2211yescharacteristic
63C22×D4×C41—21no—
64C22×D4×C41—21no—
65C22×D4×C41—21no—
66C22×D4×C41—21no—
67C22×D4×C41—21no—
68C22×D4×C41—21no—
69C22×D4×C41—21no—
70C22×D4×C41—21no—
71C22×D4×C41D411yescharacteristic
72C22×D4×C41C2311yescharacteristic
73C22×D4×C41C2311yescharacteristic
74C22×D4×C41C2311yescharacteristic
75C23×C4×C41—21no—
76C23×C4×C41C2311yescharacteristic
77C23×C4×C41C2311yescharacteristic
78C2×D8×C41—22no—
79C2×D8×C41—22no—
80C2×D8×C41—22no—
81C2×D8×C41—22no—
82C2×D8×C41—41no—
83C2×D8×C41—41no—
84C2×M16×C41—22no—
85C2×M16×C41—22no—
86C2×M16×C41—41no—
87C22×C8×C41—22no—
88C22×C8×C41—22no—
89C22×C8×C41—41no—
90C22×C8×C41C2311yescharacteristic
91C22×C8×C41C2311yescharacteristic
92C22×C8×C41C2311yescharacteristic
93C22×C8×C41C2311yescharacteristic
94#127×C41—22no—
95#127×C41—22no—
96#127×C41—44no—
97#121×C41—22no—
98#121×C41—22no—
99#121×C41—22no—
100#121×C41—22no—
101#121×C41—22no—
102#121×C41—22no—
103#121×C41—41no—
104#121×C41—41no—
105#121×C41—41no—
106#121×C41—41no—
107#121×C41—41no—
108#121×C41—41no—
109C4×D4×C41—22no—
110C4×D4×C41—22no—
111C4×D4×C41—22no—
112C4×D4×C41—22no—
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×C41D411yescharacteristic
129C2×C22⋊C4×C41D411yescharacteristic
130C2×C42×C41—21no—
131C2×C42×C41C2311yescharacteristic
132#107×C41—22no—
133#106×C41—22no—
134C4⋊C8×C41D414yescomplemented
135#102×C41—22no—
136#102×C41—22no—
137#102×C41—22no—
138#102×C41—22no—
139#102×C41—22no—
140#102×C41—41no—
141#102×C41—41no—
142#102×C41D414yescomplemented
143C22⋊C8×C41—22no—
144C22⋊C8×C41—22no—
145#97×C41—22no—
146#95×C41—21no—
147#95×C41—21no—
148#95×C41—21no—
149#95×C41—21no—
150#95×C41—21no—
151C24×C41—21no—
152C24×C41—21no—
153C24×C41—21no—
154C24×C41C2×D411yescharacteristic
155C24×C41C2×D411yescharacteristic
156C2×D4×C41—22no—
157C2×D4×C41—22no—
158C2×D4×C41—21no—
159C2×D4×C41—21no—
160C2×D4×C41—21no—
161C2×D4×C41—21no—
162C2×D4×C41—21no—
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—41no—
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—42no—
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—42no—
191C2×D4×C41—42no—
192C2×D4×C41—81no—
193C2×D4×C41—81no—
194C2×D4×C41—81no—
195C2×D4×C41—81no—
196C2×D4×C41—81no—
197C2×D4×C41—81no—
198C2×D4×C41—81no—
199C2×D4×C41—81no—
200C2×D4×C41C2×D412yes—
201C22×C4×C41—21no—
202C22×C4×C41—21no—
203C22×C4×C41—21no—
204C22×C4×C41—21no—
205C22×C4×C41—21no—
206C22×C4×C41—21no—
207C22×C4×C41—21no—
208C22×C4×C41—21no—
209C22×C4×C41—21no—
210C22×C4×C41—21no—
211C22×C4×C41—21no—
212C22×C4×C41—21no—
213C22×C4×C41—21no—
214C22×C4×C41—21no—
215C22×C4×C41—21no—
216C22×C4×C41—21no—
217C22×C4×C41—21no—
218C22×C4×C41—42no—
219C22×C4×C41—81no—
220C22×C4×C41—81no—
221C22×C4×C41C2×D411yescharacteristic
222C22×C4×C41C2×D411yescharacteristic
223C22×C4×C41C2×D411yescharacteristic
224C22×C4×C41C2×D411yescharacteristic
225C22×C4×C41C2411yescharacteristic
226D8×C41—44no—
227D8×C41—44no—
228M16×C41—44no—
229C2×C8×C41—21no—
230C2×C8×C41—21no—
231C2×C8×C41—21no—
232C2×C8×C41—21no—
233C2×C8×C41—21no—
234C2×C8×C41—21no—
235C2×C8×C41—21no—
236C2×C8×C41—21no—
237C2×C8×C41—21no—
238C2×C8×C41—44no—
239C2×C8×C41C2×D412yes—
240C2×C8×C41C2×D412yes—
241C2×C8×C41C2×D412yes—
242C4⋊C4×C41—22no—
243C4⋊C4×C41—21no—
244C4⋊C4×C41—21no—
245C4⋊C4×C41—21no—
246C4⋊C4×C41—21no—
247C4⋊C4×C41—21no—
248C4⋊C4×C41—21no—
249C4⋊C4×C41—21no—
250C4⋊C4×C41—21no—
251C4⋊C4×C41C2×D412yes—
252C4⋊C4×C41#4112yes—
253C22⋊C4×C41—22no—
254C22⋊C4×C41—22no—
255C22⋊C4×C41—42no—
256C22⋊C4×C41—42no—
257C22⋊C4×C41—42no—
258C22⋊C4×C41—42no—
259C22⋊C4×C41—42no—
260C22⋊C4×C41—42no—
261C22⋊C4×C41—42no—
262C22⋊C4×C41—81no—
263C22⋊C4×C41—81no—
264C42×C41—42no—
265C42×C41C2×D412yes—
266C42×C41#4112yes—
267C23×C41—21no—
268C23×C41—21no—
269C23×C41—21no—
270C23×C41—21no—
271C23×C41—21no—
272C23×C41—21no—
273C23×C41—21no—
274C23×C41—22no—
275C23×C41—21no—
276C23×C41—21no—
277C23×C41—21no—
278C23×C41—21no—
279C23×C41—21no—
280C23×C41—21no—
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×C41—41no—
292C23×C41—41no—
293C23×C41—41no—
294C23×C41—41no—
295C23×C41—41no—
296C23×C41—41no—
297C23×C41—41no—
298C23×C41—41no—
299C23×C41—41no—
300C23×C41—41no—
301C23×C41AGL(1,ℤ/8)12yes—
302C23×C41C22×D411yescharacteristic
303D4×C41—22no—
304D4×C41—22no—
305D4×C41—44no—
306D4×C41—41no—
307D4×C41—41no—
308D4×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—84no—
317D4×C41—84no—
318D4×C41—84no—
319D4×C41—84no—
320D4×C41—84no—
321D4×C41—84no—
322D4×C41—84no—
323D4×C41—84no—
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—22no—
333C2×C4×C41—22no—
334C2×C4×C41—21no—
335C2×C4×C41—21no—
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—41no—
344C2×C4×C41—41no—
345C2×C4×C41—41no—
346C2×C4×C41—41no—
347C2×C4×C41—41no—
348C2×C4×C41—41no—
349C2×C4×C41—41no—
350C2×C4×C41—41no—
351C2×C4×C41—41no—
352C2×C4×C41—41no—
353C2×C4×C41—41no—
354C2×C4×C41—41no—
355C2×C4×C41—41no—
356C2×C4×C41—41no—
357C2×C4×C41—84no—
358C2×C4×C41#12112yes—
359C2×C4×C41#12112yes—
360C2×C4×C41C22×D411yescharacteristic
361C2×C4×C41C22×D411yescharacteristic
362C2×C4×C41C2×#4111yescharacteristic
363C2×C4×C41C2×#4111yescharacteristic
364C2×C4×C41H(5,𝔽2)11yescharacteristic
365C2×C4×C41H(5,𝔽2)11yescharacteristic
366C8×C41—22no—
367C8×C41—22no—
368C8×C41—22no—
369C8×C41—41no—
370#25396C4111yesmaximal, characteristic, direct product factor, Sylow
371C22×C41—22no—
372C22×C41—22no—
373C22×C41—22no—
374C22×C41—41no—
375C22×C41—41no—
376C22×C41—41no—
377C22×C41—41no—
378C22×C41—41no—
379C22×C41—42no—
380C22×C41—41no—
381C22×C41—42no—
382C22×C41—41no—
383C22×C41—42no—
384C22×C41—41no—
385C22×C41—41no—
386C22×C41—41no—
387C22×C41—41no—
388C22×C41—81no—
389C22×C41—81no—
390C22×C41—81no—
391C22×C41—81no—
392C22×C41—81no—
393C22×C41—81no—
394C22×C41—81no—
395C22×C41—81no—
396C22×C41—81no—
397C22×C41—81no—
398C22×C41—81no—
399C22×C41—81no—
400C22×C41—81no—
401C22×C41—81no—
402C22×C41—81no—
403C22×C41—81no—
404C22×C41—81no—
405C22×C41—81no—
406C22×C41C2×#12111yescharacteristic
407C22×C41D4211yescharacteristic
408C22×C41#54611yescharacteristic
409C22×C41C2×AGL(1,ℤ/8)11yescharacteristic
410C22×C41#57511yescharacteristic
411C22×C41#57611yescharacteristic
412C22×C41#57611yescharacteristic
413C4×C41—22no—
414C4×C41—22no—
415C4×C41—41no—
416C4×C41—41no—
417C4×C41—42no—
418C4×C41—42no—
419C4×C41—81no—
420C4×C41—81no—
421C4×C41—81no—
422C4×C41#53211yescharacteristic
423C4×C41#54011yescharacteristic
424C4×C41D4211yescharacteristic
425C4×C41#55011yescharacteristic
426C2×#469C2×C4111yescharacteristic, complemented
427C2×#466C2×C4111yescharacteristic, complemented
428C2×#459C2×C4111yescharacteristic, complemented
429C2×#435C2×C4111yescharacteristic, complemented
430#2541C2×C4111yescharacteristic, complemented
431#2535C2×C4111yescharacteristic, complemented
432#2034C2×C4111yescharacteristic, complemented
433#2033C2×C4111yescharacteristic, complemented
434#1999C2×C4111yescharacteristic, complemented
435#1999C2×C4111yescharacteristic, complemented
436#1961C2×C4111yescharacteristic, complemented
437#1949C2×C4111yescharacteristic, complemented
438#1895C2×C4111yescharacteristic, complemented
439#1893C2×C4111yescharacteristic, complemented
440#1762C2×C4111yescharacteristic, complemented
441C2×C41—42no—
442C2×C41—81no—
443C2×C41—82no—
444C2×C41—161no—
445C2×C41—161no—
446C2×C41#242811yescharacteristic
447C2×C41#305511yescharacteristic
448C2×C41#305811yescharacteristic
449C2×C41#326411yescharacteristic
450C2×C41#326811yescharacteristic
451C2×C41#330911yescharacteristic
452C2×C41#331811yescharacteristic
453C22×D8C22×C4111yescharacteristic
454C22×D8C22×C4111yescharacteristic
455C22×M16C22×C4111yescharacteristic
456C23×C8C22×C4111yescharacteristic
457C2×#127—21no—
458C2×#127C22×C4111yescharacteristic
459C2×#121C22×C4111yescharacteristic
460C2×#121C22×C4111yescharacteristic
461C2×#121C22×C4111yescharacteristic
462C2×#121C22×C4111yescharacteristic
463C2×#121C22×C4111yescharacteristic
464C2×#121C22×C4111yescharacteristic
465C2×C4×D4C22×C4111yescharacteristic
466C2×C4×D4C22×C4111yescharacteristic
467#469—24no—
468#466—24no—
469#459—24no—
470#435—24no—
471C2×#107C22×C4111yescharacteristic
472C2×#106C22×C4111yescharacteristic
473C2×C4⋊C8C22×C4111yescharacteristic
474C2×#102C22×C4111yescharacteristic
475C2×#102C22×C4111yescharacteristic
476C2×#102C22×C4111yescharacteristic
477C2×#102C22×C4111yescharacteristic
478C2×#102C22×C4111yescharacteristic
479C2×#102C22×C4111yescharacteristic
480C2×#102C22×C4111yescharacteristic
481C2×#102C22×C4111yescharacteristic
482C2×C22⋊C8C22×C4111yescharacteristic
483C2×C22⋊C8C22×C4111yescharacteristic
484C2×#97C22×C4111yescharacteristic
485#397—21no—
486#392—21no—
487#392—21no—
488#392—21no—
489#390—21no—
490#386—21no—
491#386—21no—
492#382C22×C4111yescharacteristic
493#380C22×C4111yescharacteristic
494#380C22×C4111yescharacteristic
495C4×C4⋊C4C22×C4111yescharacteristic
496#340C22×C4111yescharacteristic
497#340C22×C4111yescharacteristic
498#340C22×C4111yescharacteristic
499#340C22×C4111yescharacteristic
500C41#2539611yescharacteristic, direct product factor, Sylow
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4D4×C4111yescharacteristic
510C22×D4C23×C4111yescharacteristic
511C22×D4C23×C4111yescharacteristic
512C22×D4C23×C4111yescharacteristic
513C23×C4—21no—
514C23×C4C23×C4111yescharacteristic
515C23×C4C23×C4111yescharacteristic
516C2×D8—22no—
517C2×D8—22no—
518C2×D8—22no—
519C2×D8—22no—
520C2×D8—41no—
521C2×D8—41no—
522C2×M16—22no—
523C2×M16—22no—
524C2×M16—41no—
525C22×C8—22no—
526C22×C8—22no—
527C22×C8—41no—
528C22×C8C23×C4111yescharacteristic
529C22×C8C23×C4111yescharacteristic
530C22×C8C23×C4111yescharacteristic
531C22×C8C23×C4111yescharacteristic
532#127—22no—
533#127—22no—
534#127—44no—
535#121—22no—
536#121—22no—
537#121—22no—
538#121—22no—
539#121—22no—
540#121—22no—
541#121—41no—
542#121—41no—
543#121—41no—
544#121—41no—
545#121—41no—
546#121—41no—
547C4×D4—22no—
548C4×D4—22no—
549C4×D4—22no—
550C4×D4—22no—
551C2×C4⋊C4D4×C4111yescharacteristic
552C2×C4⋊C4C23×C4111yescharacteristic
553C2×C4⋊C4C23×C4111yescharacteristic
554C2×C4⋊C4C23×C4111yescharacteristic
555C2×C4⋊C4C23×C4111yescharacteristic
556C2×C4⋊C4C23×C4111yescharacteristic
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4D4×C4111yescharacteristic
567C2×C22⋊C4D4×C4111yescharacteristic
568C2×C42—21no—
569C2×C42C23×C4111yescharacteristic
570#107—22no—
571#106—22no—
572C4⋊C8D4×C4114yescomplemented
573#102—22no—
574#102—22no—
575#102—22no—
576#102—22no—
577#102—22no—
578#102—41no—
579#102—41no—
580#102D4×C4114yescomplemented
581C22⋊C8—22no—
582C22⋊C8—22no—
583#97—22no—
584#95—21no—
585#95—21no—
586#95—21no—
587#95—21no—
588#95—21no—
589C24—21no—
590C24—21no—
591C24—21no—
592C24C2×D4×C4111yescharacteristic
593C24C2×D4×C4111yescharacteristic
594C2×D4—22no—
595C2×D4—22no—
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—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—41no—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4—42no—
620C2×D4—42no—
621C2×D4—42no—
622C2×D4—42no—
623C2×D4—42no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—42no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—42no—
630C2×D4—81no—
631C2×D4—81no—
632C2×D4—81no—
633C2×D4—81no—
634C2×D4—81no—
635C2×D4—81no—
636C2×D4—81no—
637C2×D4—81no—
638C2×D4C2×D4×C4112yes—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—42no—
657C22×C4—81no—
658C22×C4—81no—
659C22×C4C2×D4×C4111yescharacteristic
660C22×C4C2×D4×C4111yescharacteristic
661C22×C4C2×D4×C4111yescharacteristic
662C22×C4C2×D4×C4111yescharacteristic
663C22×C4C24×C4111yescharacteristic
664D8—44no—
665D8—44no—
666M16—44no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—44no—
677C2×C8C2×D4×C4112yes—
678C2×C8C2×D4×C4112yes—
679C2×C8C2×D4×C4112yes—
680C4⋊C4—22no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4C2×D4×C4112yes—
690C4⋊C4#41×C4112yes—
691C22⋊C4—22no—
692C22⋊C4—22no—
693C22⋊C4—42no—
694C22⋊C4—42no—
695C22⋊C4—42no—
696C22⋊C4—42no—
697C22⋊C4—42no—
698C22⋊C4—42no—
699C22⋊C4—42no—
700C22⋊C4—81no—
701C22⋊C4—81no—
702C42—42no—
703C42C2×D4×C4112yes—
704C42#41×C4112yes—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—22no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23AGL(1,ℤ/8)×C4112yes—
740C23C22×D4×C4111yescharacteristic
741D4—22no—
742D4—22no—
743D4—44no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—41no—
751D4—41no—
752D4—41no—
753D4—41no—
754D4—84no—
755D4—84no—
756D4—84no—
757D4—84no—
758D4—84no—
759D4—84no—
760D4—84no—
761D4—84no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—84no—
796C2×C4#121×C4112yes—
797C2×C4#121×C4112yes—
798C2×C4C22×D4×C4111yescharacteristic
799C2×C4C22×D4×C4111yescharacteristic
800C2×C4C2×#41×C4111yescharacteristic
801C2×C4C2×#41×C4111yescharacteristic
802C2×C4H(5,𝔽2)×C4111yescharacteristic
803C2×C4H(5,𝔽2)×C4111yescharacteristic
804C8—22no—
805C8—22no—
806C8—22no—
807C8—41no—
808C22—22no—
809C22—22no—
810C22—22no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—42no—
821C22—41no—
822C22—42no—
823C22—41no—
824C22—42no—
825C22—81no—
826C22—81no—
827C22—81no—
828C22—81no—
829C22—81no—
830C22—81no—
831C22—81no—
832C22—81no—
833C22—81no—
834C22—81no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22—81no—
840C22—81no—
841C22—81no—
842C22—81no—
843C22C2×#121×C4111yescharacteristic
844C22D42×C4111yescharacteristic
845C22C41×#54611yescharacteristic
846C22C2×AGL(1,ℤ/8)×C4111yescharacteristic
847C22C41×#57511yescharacteristic
848C22C41×#57611yescharacteristic
849C22C41×#57611yescharacteristic
850C4—22no—
851C4—22no—
852C4—42no—
853C4—41no—
854C4—41no—
855C4—42no—
856C4—81no—
857C4—81no—
858C4—81no—
859C4C41×#53211yescharacteristic
860C4C41×#54011yescharacteristic
861C4D42×C4111yescharacteristic
862C4C41×#55011yescharacteristic
863C2—42no—
864C2—81no—
865C2—82no—
866C2—161no—
867C2—161no—
868C2C41×#242811yescharacteristic
869C2C41×#305511yescharacteristic
870C2C41×#305811yescharacteristic
871C2C41×#326411yescharacteristic
872C2C41×#326811yescharacteristic
873C2C41×#330911yescharacteristic
874C2C41×#331811yescharacteristic
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×#466C2semidirect
3. C2×C41×#459C2semidirect
4. C2×C41×#435C2semidirect
5. C41×#2541C2semidirect
6. C41×#2535C2semidirect
7. C41×#2034C2semidirect
8. C41×#2033C2semidirect
9. C41×#1999C2semidirect
10. C41×#1999C2semidirect
11. C41×#1961C2semidirect
12. C41×#1949C2semidirect
13. C41×#1895C2semidirect
14. C41×#1893C2semidirect
15. C41×#1762C2semidirect
134. C4⋊C8×C41D4semidirect
142. #102×C41D4semidirect
370. #25396C41direct (N × H)
426. C2×#469C2×C41semidirect
427. C2×#466C2×C41semidirect
428. C2×#459C2×C41semidirect
429. C2×#435C2×C41semidirect
430. #2541C2×C41semidirect
431. #2535C2×C41semidirect
432. #2034C2×C41semidirect
433. #2033C2×C41semidirect
434. #1999C2×C41semidirect
435. #1999C2×C41semidirect
436. #1961C2×C41semidirect
437. #1949C2×C41semidirect
438. #1895C2×C41semidirect
439. #1893C2×C41semidirect
440. #1762C2×C41semidirect
500. C41#25396direct (N × H)
572. C4⋊C8D4×C41semidirect
580. #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×#4662
C2×C41×#4592
C2×C41×#4352
C41×#25412
C41×#25352
C41×#20342
C41×#20332
C41×#19992
C41×#19612
C41×#19492
C41×#18952
C41×#18932
C41×#17622
#2539641