Finite Group Databasebeta

← C41×#25402 #23801603

Subgroups — C41×#25402 #23801603

Order 10496.

1120 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#468C211yesmaximal, characteristic, complemented
2C2×C41×#465C211yesmaximal, characteristic, complemented
3C2×C41×#460C211yesmaximal, characteristic, complemented
4C2×C41×#435C211yesmaximal, characteristic, complemented
5C41×#2541C211yesmaximal, characteristic
6C41×#2536C211yesmaximal, characteristic, complemented
7C41×#2034C211yesmaximal, characteristic, complemented
8C41×#2033C211yesmaximal, characteristic, complemented
9C41×#2000C211yesmaximal, characteristic, complemented
10C41×#2000C211yesmaximal, characteristic, complemented
11C41×#1961C211yesmaximal, characteristic, complemented
12C41×#1949C211yesmaximal, characteristic, complemented
13C41×#1895C211yesmaximal, characteristic, complemented
14C41×#1893C211yesmaximal, characteristic, complemented
15C41×#1763C211yesmaximal, characteristic, complemented
16C22×SD16×C41C2211yescharacteristic
17C22×SD16×C41C2211yescharacteristic
18C22×M16×C41C2211yescharacteristic
19C23×C8×C41C2211yescharacteristic
20C2×#127×C41—21no—
21C2×#127×C41C2211yescharacteristic
22C2×C22⋊Q8×C41C2211yescharacteristic
23C2×C22⋊Q8×C41C2211yescharacteristic
24C2×#121×C41C2211yescharacteristic
25C2×#121×C41C2211yescharacteristic
26C2×#121×C41C2211yescharacteristic
27C2×#121×C41C2211yescharacteristic
28C2×C4×Q8×C41C2211yescharacteristic
29C2×C4×D4×C41C2211yescharacteristic
30C41×#468—24no—
31C41×#465—24no—
32C41×#460—24no—
33C41×#435—24no—
34C2×#107×C41C2211yescharacteristic
35C2×#106×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×C22⋊C8×C41C2211yescharacteristic
46C2×C22⋊C8×C41C2211yescharacteristic
47C2×#97×C41C2211yescharacteristic
48C41×#398—21no—
49C41×#394—21no—
50C41×#392—21no—
51C41×#392—21no—
52C41×#390—21no—
53C41×#388—21no—
54C41×#388—21no—
55C41×#382C2211yescharacteristic
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×C41—21no—
69C22×D4×C41—21no—
70C22×D4×C41D411yescharacteristic
71C22×D4×C41C2311yescharacteristic
72C22×D4×C41C2311yescharacteristic
73C23×C4×C41C2311yescharacteristic
74C23×C4×C41C2311yescharacteristic
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×M16×C41—22no—
82C2×M16×C41—22no—
83C2×M16×C41—41no—
84C22×C8×C41—22no—
85C22×C8×C41—22no—
86C22×C8×C41—41no—
87C22×C8×C41C2311yescharacteristic
88C22×C8×C41C2311yescharacteristic
89C22×C8×C41C2311yescharacteristic
90C22×C8×C41C2311yescharacteristic
91#127×C41—22no—
92#127×C41—22no—
93#127×C41—44no—
94C22⋊Q8×C41—22no—
95C22⋊Q8×C41—22no—
96C22⋊Q8×C41—41no—
97C22⋊Q8×C41—41no—
98#121×C41—22no—
99#121×C41—22no—
100#121×C41—22no—
101#121×C41—22no—
102#121×C41—41no—
103#121×C41—41no—
104#121×C41—41no—
105#121×C41—41no—
106C4×Q8×C41—22no—
107C4×Q8×C41—22no—
108C4×D4×C41—22no—
109C4×D4×C41—22no—
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×C41D411yescharacteristic
128C2×C22⋊C4×C41D411yescharacteristic
129C2×C42×C41—21no—
130C2×C42×C41—21no—
131C2×C42×C41C2311yescharacteristic
132#107×C41—22no—
133#106×C41—22no—
134C4⋊C8×C41D414yescomplemented
135#103×C41—22no—
136#103×C41D414yescomplemented
137#102×C41—22no—
138#102×C41—22no—
139#102×C41—22no—
140#102×C41—22no—
141#102×C41—41no—
142#102×C41—41no—
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×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×C41C2×D412yes—
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—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—81no—
189C2×D4×C41—81no—
190C2×D4×C41—81no—
191C2×D4×C41—81no—
192C2×D4×C41—81no—
193C2×D4×C41—81no—
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—21no—
207C22×C4×C41—21no—
208C22×C4×C41—21no—
209C22×C4×C41—21no—
210C22×C4×C41—21no—
211C22×C4×C41—21no—
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—
219M16×C41—44no—
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—21no—
227C2×C8×C41—21no—
228C2×C8×C41—21no—
229C2×C8×C41—44no—
230C2×C8×C41C2×D412yes—
231C2×C8×C41C2×D412yes—
232C2×C8×C41C2×D412yes—
233C4⋊C4×C41—22no—
234C4⋊C4×C41—21no—
235C4⋊C4×C41—21no—
236C4⋊C4×C41—21no—
237C4⋊C4×C41—21no—
238C4⋊C4×C41—21no—
239C4⋊C4×C41—21no—
240C4⋊C4×C41—21no—
241C4⋊C4×C41—21no—
242C4⋊C4×C41—42no—
243C4⋊C4×C41—42no—
244C4⋊C4×C41—42no—
245C4⋊C4×C41C2×D412yes—
246C4⋊C4×C41#4112yes—
247C22⋊C4×C41—22no—
248C22⋊C4×C41—22no—
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—
257C42×C41—42no—
258C42×C41—42no—
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—21no—
269C23×C41—21no—
270C23×C41—21no—
271C23×C41—21no—
272C23×C41—21no—
273C23×C41—21no—
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×C41AGL(1,ℤ/8)12yes—
289C23×C41C22×D411yescharacteristic
290Q8×C41—22no—
291Q8×C41—22no—
292Q8×C41—41no—
293Q8×C41—41no—
294D4×C41—44no—
295D4×C41—41no—
296D4×C41—41no—
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—
307D4×C41—84no—
308D4×C41—84no—
309C2×C4×C41—21no—
310C2×C4×C41—21no—
311C2×C4×C41—21no—
312C2×C4×C41—21no—
313C2×C4×C41—21no—
314C2×C4×C41—21no—
315C2×C4×C41—22no—
316C2×C4×C41—21no—
317C2×C4×C41—21no—
318C2×C4×C41—22no—
319C2×C4×C41—22no—
320C2×C4×C41—21no—
321C2×C4×C41—21no—
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—41no—
344C2×C4×C41—41no—
345C2×C4×C41#12112yes—
346C2×C4×C41#12112yes—
347C2×C4×C41C22×D411yescharacteristic
348C2×C4×C41C22×D411yescharacteristic
349C2×C4×C41C2×#4111yescharacteristic
350C2×C4×C41C2×#4111yescharacteristic
351C2×C4×C41H(5,𝔽2)11yescharacteristic
352C2×C4×C41H(5,𝔽2)11yescharacteristic
353C8×C41—22no—
354C8×C41—22no—
355C8×C41—22no—
356C8×C41—41no—
357#25402C4111yesmaximal, characteristic, direct product factor, Sylow
358C22×C41—22no—
359C22×C41—22no—
360C22×C41—22no—
361C22×C41—41no—
362C22×C41—41no—
363C22×C41—41no—
364C22×C41—41no—
365C22×C41—41no—
366C22×C41—41no—
367C22×C41—41no—
368C22×C41—41no—
369C22×C41—41no—
370C22×C41—41no—
371C22×C41—41no—
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×C41C2×#12111yescharacteristic
387C22×C41D4211yescharacteristic
388C22×C41#54611yescharacteristic
389C22×C41C2×AGL(1,ℤ/8)11yescharacteristic
390C22×C41#57511yescharacteristic
391C22×C41#57711yescharacteristic
392C22×C41#57711yescharacteristic
393C4×C41—22no—
394C4×C41—22no—
395C4×C41—41no—
396C4×C41—41no—
397C4×C41—42no—
398C4×C41—42no—
399C4×C41—42no—
400C4×C41—81no—
401C4×C41—81no—
402C4×C41—81no—
403C4×C41#53211yescharacteristic
404C4×C41#54011yescharacteristic
405C4×C41D4211yescharacteristic
406C4×C41#55011yescharacteristic
407C2×#468C2×C4111yescharacteristic, complemented
408C2×#465C2×C4111yescharacteristic, complemented
409C2×#460C2×C4111yescharacteristic, complemented
410C2×#435C2×C4111yescharacteristic, complemented
411#2541C2×C4111yescharacteristic
412#2536C2×C4111yescharacteristic, complemented
413#2034C2×C4111yescharacteristic, complemented
414#2033C2×C4111yescharacteristic, complemented
415#2000C2×C4111yescharacteristic, complemented
416#2000C2×C4111yescharacteristic, complemented
417#1961C2×C4111yescharacteristic, complemented
418#1949C2×C4111yescharacteristic, complemented
419#1895C2×C4111yescharacteristic, complemented
420#1893C2×C4111yescharacteristic, complemented
421#1763C2×C4111yescharacteristic, complemented
422C2×C41—42no—
423C2×C41—81no—
424C2×C41—161no—
425C2×C41—161no—
426C2×C41#242811yescharacteristic
427C2×C41#305511yescharacteristic
428C2×C41#305711yescharacteristic
429C2×C41#326511yescharacteristic
430C2×C41#327111yescharacteristic
431C2×C41#331011yescharacteristic
432C2×C41#331711yescharacteristic
433C22×SD16C22×C4111yescharacteristic
434C22×SD16C22×C4111yescharacteristic
435C22×M16C22×C4111yescharacteristic
436C23×C8C22×C4111yescharacteristic
437C2×#127—21no—
438C2×#127C22×C4111yescharacteristic
439C2×C22⋊Q8C22×C4111yescharacteristic
440C2×C22⋊Q8C22×C4111yescharacteristic
441C2×#121C22×C4111yescharacteristic
442C2×#121C22×C4111yescharacteristic
443C2×#121C22×C4111yescharacteristic
444C2×#121C22×C4111yescharacteristic
445C2×C4×Q8C22×C4111yescharacteristic
446C2×C4×D4C22×C4111yescharacteristic
447#468—24no—
448#465—24no—
449#460—24no—
450#435—24no—
451C2×#107C22×C4111yescharacteristic
452C2×#106C22×C4111yescharacteristic
453C2×C4⋊C8C22×C4111yescharacteristic
454C2×#103C22×C4111yescharacteristic
455C2×#103C22×C4111yescharacteristic
456C2×#102C22×C4111yescharacteristic
457C2×#102C22×C4111yescharacteristic
458C2×#102C22×C4111yescharacteristic
459C2×#102C22×C4111yescharacteristic
460C2×#102C22×C4111yescharacteristic
461C2×#102C22×C4111yescharacteristic
462C2×C22⋊C8C22×C4111yescharacteristic
463C2×C22⋊C8C22×C4111yescharacteristic
464C2×#97C22×C4111yescharacteristic
465#398—21no—
466#394—21no—
467#392—21no—
468#392—21no—
469#390—21no—
470#388—21no—
471#388—21no—
472#382C22×C4111yescharacteristic
473#380C22×C4111yescharacteristic
474#380C22×C4111yescharacteristic
475C4×C4⋊C4C22×C4111yescharacteristic
476#340C22×C4111yescharacteristic
477#340C22×C4111yescharacteristic
478#340C22×C4111yescharacteristic
479#340C22×C4111yescharacteristic
480C41#2540211yescharacteristic, direct product factor, Sylow
481C22×Q8C23×C4111yescharacteristic
482C22×D4—21no—
483C22×D4—21no—
484C22×D4—21no—
485C22×D4—21no—
486C22×D4—21no—
487C22×D4—21no—
488C22×D4D4×C4111yescharacteristic
489C22×D4C23×C4111yescharacteristic
490C22×D4C23×C4111yescharacteristic
491C23×C4C23×C4111yescharacteristic
492C23×C4C23×C4111yescharacteristic
493C2×SD16—22no—
494C2×SD16—22no—
495C2×SD16—22no—
496C2×SD16—22no—
497C2×SD16—41no—
498C2×SD16—41no—
499C2×M16—22no—
500C2×M16—22no—
501C2×M16—41no—
502C22×C8—22no—
503C22×C8—22no—
504C22×C8—41no—
505C22×C8C23×C4111yescharacteristic
506C22×C8C23×C4111yescharacteristic
507C22×C8C23×C4111yescharacteristic
508C22×C8C23×C4111yescharacteristic
509#127—22no—
510#127—22no—
511#127—44no—
512C22⋊Q8—22no—
513C22⋊Q8—22no—
514C22⋊Q8—41no—
515C22⋊Q8—41no—
516#121—22no—
517#121—22no—
518#121—22no—
519#121—22no—
520#121—41no—
521#121—41no—
522#121—41no—
523#121—41no—
524C4×Q8—22no—
525C4×Q8—22no—
526C4×D4—22no—
527C4×D4—22no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4D4×C4111yescharacteristic
532C2×C4⋊C4C23×C4111yescharacteristic
533C2×C4⋊C4C23×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⋊C4D4×C4111yescharacteristic
546C2×C22⋊C4D4×C4111yescharacteristic
547C2×C42—21no—
548C2×C42—21no—
549C2×C42C23×C4111yescharacteristic
550#107—22no—
551#106—22no—
552C4⋊C8D4×C4114yescomplemented
553#103—22no—
554#103D4×C4114yescomplemented
555#102—22no—
556#102—22no—
557#102—22no—
558#102—22no—
559#102—41no—
560#102—41no—
561C22⋊C8—22no—
562C22⋊C8—22no—
563#97—22no—
564#95—21no—
565#95—21no—
566#95—21no—
567#95—21no—
568#95—21no—
569C24—21no—
570C24—21no—
571C24C2×D4×C4111yescharacteristic
572C24C2×D4×C4111yescharacteristic
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8C2×D4×C4112yes—
579C2×D4—22no—
580C2×D4—22no—
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—21no—
592C2×D4—21no—
593C2×D4—41no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—42no—
601C2×D4—42no—
602C2×D4—42no—
603C2×D4—42no—
604C2×D4—42no—
605C2×D4—42no—
606C2×D4—81no—
607C2×D4—81no—
608C2×D4—81no—
609C2×D4—81no—
610C2×D4—81no—
611C2×D4—81no—
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—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4C2×D4×C4111yescharacteristic
631C22×C4C2×D4×C4111yescharacteristic
632C22×C4C2×D4×C4111yescharacteristic
633C22×C4C2×D4×C4111yescharacteristic
634C22×C4C24×C4111yescharacteristic
635SD16—44no—
636SD16—44no—
637M16—44no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—44no—
648C2×C8C2×D4×C4112yes—
649C2×C8C2×D4×C4112yes—
650C2×C8C2×D4×C4112yes—
651C4⋊C4—22no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—42no—
661C4⋊C4—42no—
662C4⋊C4—42no—
663C4⋊C4C2×D4×C4112yes—
664C4⋊C4#41×C4112yes—
665C22⋊C4—22no—
666C22⋊C4—22no—
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—42no—
676C42—42no—
677C42C2×D4×C4112yes—
678C42#41×C4112yes—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
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—
705C23—41no—
706C23AGL(1,ℤ/8)×C4112yes—
707C23C22×D4×C4111yescharacteristic
708Q8—22no—
709Q8—22no—
710Q8—41no—
711Q8—41no—
712D4—44no—
713D4—41no—
714D4—41no—
715D4—41no—
716D4—41no—
717D4—41no—
718D4—41no—
719D4—41no—
720D4—41no—
721D4—84no—
722D4—84no—
723D4—84no—
724D4—84no—
725D4—84no—
726D4—84no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—22no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—21no—
739C2×C4—21no—
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—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4#121×C4112yes—
764C2×C4#121×C4112yes—
765C2×C4C22×D4×C4111yescharacteristic
766C2×C4C22×D4×C4111yescharacteristic
767C2×C4C2×#41×C4111yescharacteristic
768C2×C4C2×#41×C4111yescharacteristic
769C2×C4H(5,𝔽2)×C4111yescharacteristic
770C2×C4H(5,𝔽2)×C4111yescharacteristic
771C8—22no—
772C8—22no—
773C8—22no—
774C8—41no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
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—
803C22C2×#121×C4111yescharacteristic
804C22D42×C4111yescharacteristic
805C22C41×#54611yescharacteristic
806C22C2×AGL(1,ℤ/8)×C4111yescharacteristic
807C22C41×#57511yescharacteristic
808C22C41×#57711yescharacteristic
809C22C41×#57711yescharacteristic
810C4—22no—
811C4—22no—
812C4—42no—
813C4—41no—
814C4—41no—
815C4—42no—
816C4—42no—
817C4—81no—
818C4—81no—
819C4—81no—
820C4C41×#53211yescharacteristic
821C4C41×#54011yescharacteristic
822C4D42×C4111yescharacteristic
823C4C41×#55011yescharacteristic
824C2—42no—
825C2—81no—
826C2—161no—
827C2—161no—
828C2C41×#242811yescharacteristic
829C2C41×#305511yescharacteristic
830C2C41×#305711yescharacteristic
831C2C41×#326511yescharacteristic
832C2C41×#327111yescharacteristic
833C2C41×#331011yescharacteristic
834C2C41×#331711yescharacteristic
subgroupG/H
center, socleC23×C41C22×D4
commutator, Frattini, cosocleC22×C4C24×C41
prime radicalC41×#2541C2
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×#468C2semidirect
2. C2×C41×#465C2semidirect
3. C2×C41×#460C2semidirect
4. C2×C41×#435C2semidirect
6. C41×#2536C2semidirect
7. C41×#2034C2semidirect
8. C41×#2033C2semidirect
9. C41×#2000C2semidirect
10. C41×#2000C2semidirect
11. C41×#1961C2semidirect
12. C41×#1949C2semidirect
13. C41×#1895C2semidirect
14. C41×#1893C2semidirect
15. C41×#1763C2semidirect
134. C4⋊C8×C41D4semidirect
136. #103×C41D4semidirect
357. #25402C41direct (N × H)
407. C2×#468C2×C41semidirect
408. C2×#465C2×C41semidirect
409. C2×#460C2×C41semidirect
410. C2×#435C2×C41semidirect
412. #2536C2×C41semidirect
413. #2034C2×C41semidirect
414. #2033C2×C41semidirect
415. #2000C2×C41semidirect
416. #2000C2×C41semidirect
417. #1961C2×C41semidirect
418. #1949C2×C41semidirect
419. #1895C2×C41semidirect
420. #1893C2×C41semidirect
421. #1763C2×C41semidirect
480. C41#25402direct (N × H)
552. C4⋊C8D4×C41semidirect
554. #103D4×C41semidirect

Maximal subgroups

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

subgroupindex
C2×C41×#4682
C2×C41×#4652
C2×C41×#4602
C2×C41×#4352
C41×#25412
C41×#25362
C41×#20342
C41×#20332
C41×#20002
C41×#19612
C41×#19492
C41×#18952
C41×#18932
C41×#17632
#2540241