Finite Group Databasebeta

← C41×#24448 #23800649

Subgroups — C41×#24448 #23800649

Order 10496.

1888 conjugacy classes of subgroups.

The subgroup lattice has 990 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C41C211yesmaximal, characteristic
2C2×C41×#468C211yesmaximal, characteristic, complemented
3C2×C41×#450C211yesmaximal, characteristic, complemented
4C2×C41×#450C211yesmaximal, characteristic, complemented
5C2×C41×#418C211yesmaximal, characteristic, complemented
6C41×#2415C211yesmaximal, characteristic, complemented
7C41×#2041C211yesmaximal, characteristic, complemented
8C41×#2033C211yesmaximal, characteristic, complemented
9C41×#2014C211yesmaximal, characteristic, complemented
10C41×#2000C211yesmaximal, characteristic, complemented
11C41×#1877C211yesmaximal, characteristic, complemented
12C41×#1875C211yesmaximal, characteristic, complemented
13C41×#1870C211yesmaximal, characteristic, complemented
14C41×#1862C211yesmaximal, characteristic, complemented
15C41×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C41—21no—
17C23×D4×C41C2211yescharacteristic
18C23×D4×C41C2211yescharacteristic
19C22×SD16×C41C2211yescharacteristic
20C22×SD16×C41C2211yescharacteristic, complemented
21C22×SD16×C41C2211yescharacteristic, complemented
22C22×M16×C41C2211yescharacteristic, complemented
23D42×C41—24no—
24D42×C41—24no—
25C2×#127×C41C2211yescharacteristic
26C2×C22⋊Q8×C41C2211yescharacteristic, complemented
27C2×C22⋊Q8×C41C2211yescharacteristic, complemented
28C2×#121×C41—21no—
29C2×#121×C41C2211yescharacteristic
30C2×#121×C41C2211yescharacteristic
31C2×#120×C41—21no—
32C2×#120×C41—21no—
33C2×C4×D4×C41C2211yescharacteristic
34C2×C4×D4×C41C2211yescharacteristic
35C2×#117×C41C2211yescharacteristic, complemented
36C41×#468—24no—
37C41×#450—24no—
38C41×#450—24no—
39C2×#107×C41C2211yescharacteristic, complemented
40C41×#418—24no—
41C2×#103×C41C2211yescharacteristic, complemented
42C2×#102×C41C2211yescharacteristic
43C2×#102×C41C2211yescharacteristic
44C2×#102×C41C2211yescharacteristic
45C2×#102×C41C2211yescharacteristic, complemented
46C2×#102×C41C2211yescharacteristic, complemented
47C2×#102×C41C2211yescharacteristic, complemented
48C2×#102×C41C2211yescharacteristic, complemented
49C2×#102×C41C2211yescharacteristic, complemented
50C2×#102×C41C2211yescharacteristic, complemented
51C2×C22⋊C8×C41C2211yescharacteristic, complemented
52C2×C22⋊C8×C41C2211yescharacteristic, complemented
53C2×C22⋊C8×C41C2211yescharacteristic, complemented
54C41×#397—21no—
55C41×#394—21no—
56C41×#391C2211yescharacteristic, complemented
57C41×#389—21no—
58C41×#389C2211yescharacteristic, complemented
59C41×#388—21no—
60C41×#380C2211yescharacteristic, complemented
61C41×#340C2211yescharacteristic, complemented
62C41×#340C2211yescharacteristic, complemented
63C41×#336C2211yescharacteristic, complemented
64C41×#336C2211yescharacteristic, complemented
65C25×C41—21no—
66C25×C41—21no—
67C22×Q8×C41C2311yescharacteristic
68C22×D4×C41—22no—
69C22×D4×C41—22no—
70C22×D4×C41—28no—
71C22×D4×C41—21no—
72C22×D4×C41—21no—
73C22×D4×C41—22no—
74C22×D4×C41—22no—
75C22×D4×C41—22no—
76C22×D4×C41—22no—
77C22×D4×C41—21no—
78C22×D4×C41—21no—
79C22×D4×C41—21no—
80C22×D4×C41—22no—
81C22×D4×C41—21no—
82C22×D4×C41—41no—
83C22×D4×C41—41no—
84C22×D4×C41—41no—
85C22×D4×C41—41no—
86C22×D4×C41—44no—
87C22×D4×C41—44no—
88C22×D4×C41D411yescharacteristic
89C22×D4×C41D414yes—
90C22×D4×C41C2311yescharacteristic
91C22×D4×C41C2311yescharacteristic
92C22×D4×C41C2311yescharacteristic
93C23×C4×C41—21no—
94C23×C4×C41C2311yescharacteristic
95C23×C4×C41C2311yescharacteristic
96C2×SD16×C41—22no—
97C2×SD16×C41—22no—
98C2×SD16×C41—22no—
99C2×SD16×C41—22no—
100C2×SD16×C41—22no—
101C2×SD16×C41—22no—
102C2×SD16×C41—41no—
103C2×SD16×C41—41no—
104C2×SD16×C41—41no—
105C2×M16×C41—22no—
106C2×M16×C41—22no—
107C2×M16×C41—41no—
108C22×C8×C41C2311yescharacteristic
109C22×C8×C41C2311yescharacteristic
110C22×C8×C41C2311yescharacteristic
111C22×C8×C41C2311yescharacteristic
112#127×C41—22no—
113#127×C41—22no—
114C22⋊Q8×C41—22no—
115C22⋊Q8×C41—22no—
116C22⋊Q8×C41—22no—
117C22⋊Q8×C41—41no—
118#121×C41—28no—
119#121×C41—22no—
120#121×C41—22no—
121#121×C41—22no—
122#121×C41D414yes—
123#120×C41—28no—
124#120×C41—28no—
125C4×D4×C41—22no—
126C4×D4×C41—22no—
127C4×D4×C41—22no—
128C4×D4×C41—22no—
129#117×C41—22no—
130#117×C41—41no—
131C2×C4⋊C4×C41—21no—
132C2×C4⋊C4×C41—21no—
133C2×C4⋊C4×C41—21no—
134C2×C4⋊C4×C41D411yescharacteristic
135C2×C4⋊C4×C41C2311yescharacteristic
136C2×C4⋊C4×C41C2311yescharacteristic
137C2×C4⋊C4×C41C2311yescharacteristic
138C2×C4⋊C4×C41C2311yescharacteristic
139C2×C22⋊C4×C41—21no—
140C2×C22⋊C4×C41—21no—
141C2×C22⋊C4×C41—21no—
142C2×C22⋊C4×C41—21no—
143C2×C22⋊C4×C41—21no—
144C2×C22⋊C4×C41—21no—
145C2×C22⋊C4×C41—21no—
146C2×C22⋊C4×C41D411yescharacteristic
147C2×C22⋊C4×C41D411yescharacteristic
148C2×C42×C41—21no—
149C2×C42×C41C2311yescharacteristic
150#107×C41—22no—
151#103×C41—22no—
152#102×C41—22no—
153#102×C41—22no—
154#102×C41—22no—
155#102×C41—22no—
156#102×C41—22no—
157#102×C41—22no—
158#102×C41—22no—
159#102×C41—41no—
160#102×C41D414yescomplemented
161C22⋊C8×C41—22no—
162C22⋊C8×C41—22no—
163C22⋊C8×C41—41no—
164#95×C41—21no—
165#95×C41—21no—
166#95×C41—21no—
167#95×C41—21no—
168C24×C41—21no—
169C24×C41—24no—
170C24×C41—21no—
171C24×C41—21no—
172C24×C41—24no—
173C24×C41—42no—
174C24×C41—42no—
175C24×C41—42no—
176C24×C41—42no—
177C24×C41—42no—
178C24×C41—42no—
179C24×C41—42no—
180C24×C41—42no—
181C24×C41—81no—
182C24×C41—81no—
183C24×C41—81no—
184C24×C41—81no—
185C24×C41C2×D411yescharacteristic
186C24×C41C2×D411yescharacteristic
187C2×Q8×C41—21no—
188C2×Q8×C41—21no—
189C2×Q8×C41—21no—
190C2×Q8×C41—21no—
191C2×Q8×C41—21no—
192C2×Q8×C41—21no—
193C2×D4×C41—22no—
194C2×D4×C41—22no—
195C2×D4×C41—28no—
196C2×D4×C41—24no—
197C2×D4×C41—24no—
198C2×D4×C41—24no—
199C2×D4×C41—24no—
200C2×D4×C41—24no—
201C2×D4×C41—24no—
202C2×D4×C41—22no—
203C2×D4×C41—21no—
204C2×D4×C41—21no—
205C2×D4×C41—21no—
206C2×D4×C41—21no—
207C2×D4×C41—21no—
208C2×D4×C41—21no—
209C2×D4×C41—21no—
210C2×D4×C41—21no—
211C2×D4×C41—21no—
212C2×D4×C41—21no—
213C2×D4×C41—21no—
214C2×D4×C41—21no—
215C2×D4×C41—21no—
216C2×D4×C41—44no—
217C2×D4×C41—44no—
218C2×D4×C41—44no—
219C2×D4×C41—42no—
220C2×D4×C41—42no—
221C2×D4×C41—42no—
222C2×D4×C41—42no—
223C2×D4×C41—42no—
224C2×D4×C41—44no—
225C2×D4×C41—44no—
226C2×D4×C41—432no—
227C2×D4×C41—44no—
228C2×D4×C41—42no—
229C2×D4×C41—42no—
230C2×D4×C41—42no—
231C2×D4×C41—42no—
232C2×D4×C41—44no—
233C2×D4×C41—42no—
234C2×D4×C41—81no—
235C2×D4×C41—81no—
236C2×D4×C41C2×D412yes—
237C2×D4×C41C2×D412yes—
238C2×D4×C41C2×D412yes—
239C2×D4×C41C2×D412yes—
240C2×D4×C41#4112yes—
241C22×C4×C41—21no—
242C22×C4×C41—21no—
243C22×C4×C41—21no—
244C22×C4×C41—21no—
245C22×C4×C41—24no—
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×C41—21no—
254C22×C4×C41—21no—
255C22×C4×C41—21no—
256C22×C4×C41—21no—
257C22×C4×C41—42no—
258C22×C4×C41—42no—
259C22×C4×C41C2×D411yescharacteristic
260C22×C4×C41C2×D411yescharacteristic
261C22×C4×C41C2×D411yescharacteristic
262C22×C4×C41C2×D412yes—
263C22×C4×C41C2×D412yes—
264C22×C4×C41C2×D411yescharacteristic
265C22×C4×C41C2411yescharacteristic
266SD16×C41—44no—
267SD16×C41—44no—
268SD16×C41—44no—
269M16×C41—44no—
270C2×C8×C41—21no—
271C2×C8×C41—21no—
272C2×C8×C41—21no—
273C2×C8×C41—21no—
274C2×C8×C41—21no—
275C2×C8×C41—21no—
276C2×C8×C41—21no—
277C2×C8×C41—21no—
278C2×C8×C41—21no—
279C2×C8×C41—21no—
280C2×C8×C41—21no—
281C2×C8×C41C2×D412yescomplemented
282C4⋊C4×C41—22no—
283C4⋊C4×C41—21no—
284C4⋊C4×C41—21no—
285C4⋊C4×C41—21no—
286C4⋊C4×C41—21no—
287C4⋊C4×C41—21no—
288C4⋊C4×C41—21no—
289C4⋊C4×C41—42no—
290C4⋊C4×C41—42no—
291C4⋊C4×C41—42no—
292C4⋊C4×C41C2×D412yes—
293C4⋊C4×C41C2×D412yescomplemented
294C22⋊C4×C41—24no—
295C22⋊C4×C41—24no—
296C22⋊C4×C41—22no—
297C22⋊C4×C41—24no—
298C22⋊C4×C41—22no—
299C22⋊C4×C41—42no—
300C22⋊C4×C41—42no—
301C22⋊C4×C41—42no—
302C22⋊C4×C41—42no—
303C42×C41—21no—
304C42×C41—21no—
305C42×C41—42no—
306C23×C41—21no—
307C23×C41—22no—
308C23×C41—21no—
309C23×C41—21no—
310C23×C41—22no—
311C23×C41—21no—
312C23×C41—21no—
313C23×C41—22no—
314C23×C41—21no—
315C23×C41—21no—
316C23×C41—21no—
317C23×C41—21no—
318C23×C41—21no—
319C23×C41—21no—
320C23×C41—21no—
321C23×C41—22no—
322C23×C41—22no—
323C23×C41—48no—
324C23×C41—48no—
325C23×C41—48no—
326C23×C41—48no—
327C23×C41—41no—
328C23×C41—41no—
329C23×C41—41no—
330C23×C41—41no—
331C23×C41—41no—
332C23×C41—41no—
333C23×C41—41no—
334C23×C41—41no—
335C23×C41—41no—
336C23×C41—41no—
337C23×C41—41no—
338C23×C41—41no—
339C23×C41—41no—
340C23×C41—41no—
341C23×C41—41no—
342C23×C41—41no—
343C23×C41—84no—
344C23×C41—84no—
345C23×C41—84no—
346C23×C41—84no—
347C23×C41—84no—
348C23×C41—84no—
349C23×C41—84no—
350C23×C41—84no—
351C23×C41—84no—
352C23×C41—84no—
353C23×C41#12012yes—
354C23×C41AGL(1,ℤ/8)12yes—
355C23×C41C22×D411yescharacteristic
356Q8×C41—41no—
357Q8×C41—41no—
358Q8×C41—41no—
359Q8×C41—41no—
360D4×C41—28no—
361D4×C41—22no—
362D4×C41—22no—
363D4×C41—22no—
364D4×C41—22no—
365D4×C41—22no—
366D4×C41—22no—
367D4×C41—22no—
368D4×C41—48no—
369D4×C41—48no—
370D4×C41—48no—
371D4×C41—48no—
372D4×C41—48no—
373D4×C41—41no—
374D4×C41—41no—
375D4×C41—41no—
376D4×C41—41no—
377D4×C41—84no—
378D4×C41#12114yes—
379C2×C4×C41—21no—
380C2×C4×C41—21no—
381C2×C4×C41—21no—
382C2×C4×C41—21no—
383C2×C4×C41—22no—
384C2×C4×C41—22no—
385C2×C4×C41—22no—
386C2×C4×C41—22no—
387C2×C4×C41—21no—
388C2×C4×C41—21no—
389C2×C4×C41—22no—
390C2×C4×C41—22no—
391C2×C4×C41—21no—
392C2×C4×C41—21no—
393C2×C4×C41—21no—
394C2×C4×C41—21no—
395C2×C4×C41—48no—
396C2×C4×C41—41no—
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—41no—
410C2×C4×C41—41no—
411C2×C4×C41—41no—
412C2×C4×C41—41no—
413C2×C4×C41#12012yes—
414C2×C4×C41AGL(1,ℤ/8)12yes—
415C2×C4×C41C22×D411yescharacteristic
416C2×C4×C41C22×D411yescharacteristic
417C2×C4×C41C22×D411yescharacteristic
418C2×C4×C41C2×#4111yescharacteristic
419C2×C4×C41H(5,𝔽2)11yescharacteristic
420C2×C4×C41H(5,𝔽2)11yescharacteristic
421C8×C41—22no—
422C8×C41—41no—
423C8×C41—41no—
424C8×C41—41no—
425#24448C4111yesmaximal, characteristic, direct product factor, Sylow
426C22×C41—22no—
427C22×C41—24no—
428C22×C41—22no—
429C22×C41—22no—
430C22×C41—22no—
431C22×C41—22no—
432C22×C41—22no—
433C22×C41—41no—
434C22×C41—42no—
435C22×C41—41no—
436C22×C41—42no—
437C22×C41—41no—
438C22×C41—42no—
439C22×C41—41no—
440C22×C41—41no—
441C22×C41—42no—
442C22×C41—41no—
443C22×C41—42no—
444C22×C41—41no—
445C22×C41—41no—
446C22×C41—42no—
447C22×C41—42no—
448C22×C41—42no—
449C22×C41—42no—
450C22×C41—42no—
451C22×C41—42no—
452C22×C41—42no—
453C22×C41—816no—
454C22×C41—816no—
455C22×C41—81no—
456C22×C41—81no—
457C22×C41—81no—
458C22×C41—81no—
459C22×C41—81no—
460C22×C41—81no—
461C22×C41—81no—
462C22×C41—81no—
463C22×C41C2×#12011yescharacteristic
464C22×C41D4211yescharacteristic
465C22×C41#54611yescharacteristic
466C22×C41C2×AGL(1,ℤ/8)11yescharacteristic
467C22×C41C2×AGL(1,ℤ/8)11yescharacteristic
468C22×C41#57711yescharacteristic
469C22×C41#57711yescharacteristic
470C4×C41—22no—
471C4×C41—22no—
472C4×C41—41no—
473C4×C41—42no—
474C4×C41—41no—
475C4×C41—42no—
476C4×C41—81no—
477C4×C41—81no—
478C4×C41—81no—
479C4×C41C2×#12111yescharacteristic
480C4×C41#53411yescharacteristic
481C4×C41D4211yescharacteristic
482C4×C41#54611yescharacteristic
483C2×D42C2×C4111yescharacteristic
484C2×#468C2×C4111yescharacteristic, complemented
485C2×#450C2×C4111yescharacteristic, complemented
486C2×#450C2×C4111yescharacteristic, complemented
487C2×#418C2×C4111yescharacteristic, complemented
488#2415C2×C4111yescharacteristic, complemented
489#2041C2×C4111yescharacteristic, complemented
490#2033C2×C4111yescharacteristic, complemented
491#2014C2×C4111yescharacteristic, complemented
492#2000C2×C4111yescharacteristic, complemented
493#1877C2×C4111yescharacteristic, complemented
494#1875C2×C4111yescharacteristic, complemented
495#1870C2×C4111yescharacteristic, complemented
496#1862C2×C4111yescharacteristic, complemented
497#1786C2×C4111yescharacteristic, complemented
498C2×C41—42no—
499C2×C41—42no—
500C2×C41—44no—
501C2×C41—82no—
502C2×C41—82no—
503C2×C41#241011yescharacteristic
504C2×C41#300311yescharacteristic
505C2×C41#300911yescharacteristic
506C2×C41#326511yescharacteristic
507C2×C41#327211yescharacteristic
508C2×C41#331011yescharacteristic
509C2×C41#332411yescharacteristic
510C23×D4—21no—
511C23×D4C22×C4111yescharacteristic
512C23×D4C22×C4111yescharacteristic
513C22×SD16C22×C4111yescharacteristic
514C22×SD16C22×C4111yescharacteristic, complemented
515C22×SD16C22×C4111yescharacteristic, complemented
516C22×M16C22×C4111yescharacteristic, complemented
517D42—24no—
518D42—24no—
519C2×#127C22×C4111yescharacteristic
520C2×C22⋊Q8C22×C4111yescharacteristic, complemented
521C2×C22⋊Q8C22×C4111yescharacteristic, complemented
522C2×#121—21no—
523C2×#121C22×C4111yescharacteristic
524C2×#121C22×C4111yescharacteristic
525C2×#120—21no—
526C2×#120—21no—
527C2×C4×D4C22×C4111yescharacteristic
528C2×C4×D4C22×C4111yescharacteristic
529C2×#117C22×C4111yescharacteristic, complemented
530#468—24no—
531#450—24no—
532#450—24no—
533C2×#107C22×C4111yescharacteristic, complemented
534#418—24no—
535C2×#103C22×C4111yescharacteristic, complemented
536C2×#102C22×C4111yescharacteristic
537C2×#102C22×C4111yescharacteristic
538C2×#102C22×C4111yescharacteristic
539C2×#102C22×C4111yescharacteristic, complemented
540C2×#102C22×C4111yescharacteristic, complemented
541C2×#102C22×C4111yescharacteristic, complemented
542C2×#102C22×C4111yescharacteristic, complemented
543C2×#102C22×C4111yescharacteristic, complemented
544C2×#102C22×C4111yescharacteristic, complemented
545C2×C22⋊C8C22×C4111yescharacteristic, complemented
546C2×C22⋊C8C22×C4111yescharacteristic, complemented
547C2×C22⋊C8C22×C4111yescharacteristic, complemented
548#397—21no—
549#394—21no—
550#391C22×C4111yescharacteristic, complemented
551#389—21no—
552#389C22×C4111yescharacteristic, complemented
553#388—21no—
554#380C22×C4111yescharacteristic, complemented
555#340C22×C4111yescharacteristic, complemented
556#340C22×C4111yescharacteristic, complemented
557#336C22×C4111yescharacteristic, complemented
558#336C22×C4111yescharacteristic, complemented
559C41#2444811yescharacteristic, direct product factor, Sylow
560C25—21no—
561C25—21no—
562C22×Q8C23×C4111yescharacteristic
563C22×D4—22no—
564C22×D4—22no—
565C22×D4—28no—
566C22×D4—21no—
567C22×D4—21no—
568C22×D4—22no—
569C22×D4—22no—
570C22×D4—22no—
571C22×D4—22no—
572C22×D4—21no—
573C22×D4—21no—
574C22×D4—21no—
575C22×D4—22no—
576C22×D4—21no—
577C22×D4—41no—
578C22×D4—41no—
579C22×D4—41no—
580C22×D4—41no—
581C22×D4—44no—
582C22×D4—44no—
583C22×D4D4×C4111yescharacteristic
584C22×D4D4×C4114yes—
585C22×D4C23×C4111yescharacteristic
586C22×D4C23×C4111yescharacteristic
587C22×D4C23×C4111yescharacteristic
588C23×C4—21no—
589C23×C4C23×C4111yescharacteristic
590C23×C4C23×C4111yescharacteristic
591C2×SD16—22no—
592C2×SD16—22no—
593C2×SD16—22no—
594C2×SD16—22no—
595C2×SD16—22no—
596C2×SD16—22no—
597C2×SD16—41no—
598C2×SD16—41no—
599C2×SD16—41no—
600C2×M16—22no—
601C2×M16—22no—
602C2×M16—41no—
603C22×C8C23×C4111yescharacteristic
604C22×C8C23×C4111yescharacteristic
605C22×C8C23×C4111yescharacteristic
606C22×C8C23×C4111yescharacteristic
607#127—22no—
608#127—22no—
609C22⋊Q8—22no—
610C22⋊Q8—22no—
611C22⋊Q8—22no—
612C22⋊Q8—41no—
613#121—28no—
614#121—22no—
615#121—22no—
616#121—22no—
617#121D4×C4114yes—
618#120—28no—
619#120—28no—
620C4×D4—22no—
621C4×D4—22no—
622C4×D4—22no—
623C4×D4—22no—
624#117—22no—
625#117—41no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4D4×C4111yescharacteristic
630C2×C4⋊C4C23×C4111yescharacteristic
631C2×C4⋊C4C23×C4111yescharacteristic
632C2×C4⋊C4C23×C4111yescharacteristic
633C2×C4⋊C4C23×C4111yescharacteristic
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4D4×C4111yescharacteristic
642C2×C22⋊C4D4×C4111yescharacteristic
643C2×C42—21no—
644C2×C42C23×C4111yescharacteristic
645#107—22no—
646#103—22no—
647#102—22no—
648#102—22no—
649#102—22no—
650#102—22no—
651#102—22no—
652#102—22no—
653#102—22no—
654#102—41no—
655#102D4×C4114yescomplemented
656C22⋊C8—22no—
657C22⋊C8—22no—
658C22⋊C8—41no—
659#95—21no—
660#95—21no—
661#95—21no—
662#95—21no—
663C24—21no—
664C24—24no—
665C24—21no—
666C24—21no—
667C24—24no—
668C24—42no—
669C24—42no—
670C24—42no—
671C24—42no—
672C24—42no—
673C24—42no—
674C24—42no—
675C24—42no—
676C24—81no—
677C24—81no—
678C24—81no—
679C24—81no—
680C24C2×D4×C4111yescharacteristic
681C24C2×D4×C4111yescharacteristic
682C2×Q8—21no—
683C2×Q8—21no—
684C2×Q8—21no—
685C2×Q8—21no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×D4—22no—
689C2×D4—22no—
690C2×D4—28no—
691C2×D4—24no—
692C2×D4—24no—
693C2×D4—24no—
694C2×D4—24no—
695C2×D4—24no—
696C2×D4—24no—
697C2×D4—22no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
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—44no—
712C2×D4—44no—
713C2×D4—44no—
714C2×D4—42no—
715C2×D4—42no—
716C2×D4—42no—
717C2×D4—42no—
718C2×D4—42no—
719C2×D4—44no—
720C2×D4—44no—
721C2×D4—432no—
722C2×D4—44no—
723C2×D4—42no—
724C2×D4—42no—
725C2×D4—42no—
726C2×D4—42no—
727C2×D4—44no—
728C2×D4—42no—
729C2×D4—81no—
730C2×D4—81no—
731C2×D4C2×D4×C4112yes—
732C2×D4C2×D4×C4112yes—
733C2×D4C2×D4×C4112yes—
734C2×D4C2×D4×C4112yes—
735C2×D4#41×C4112yes—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—24no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—42no—
753C22×C4—42no—
754C22×C4C2×D4×C4111yescharacteristic
755C22×C4C2×D4×C4111yescharacteristic
756C22×C4C2×D4×C4111yescharacteristic
757C22×C4C2×D4×C4112yes—
758C22×C4C2×D4×C4112yes—
759C22×C4C2×D4×C4111yescharacteristic
760C22×C4C24×C4111yescharacteristic
761SD16—44no—
762SD16—44no—
763SD16—44no—
764M16—44no—
765C2×C8—21no—
766C2×C8—21no—
767C2×C8—21no—
768C2×C8—21no—
769C2×C8—21no—
770C2×C8—21no—
771C2×C8—21no—
772C2×C8—21no—
773C2×C8—21no—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8C2×D4×C4112yescomplemented
777C4⋊C4—22no—
778C4⋊C4—21no—
779C4⋊C4—21no—
780C4⋊C4—21no—
781C4⋊C4—21no—
782C4⋊C4—21no—
783C4⋊C4—21no—
784C4⋊C4—42no—
785C4⋊C4—42no—
786C4⋊C4—42no—
787C4⋊C4C2×D4×C4112yes—
788C4⋊C4C2×D4×C4112yescomplemented
789C22⋊C4—24no—
790C22⋊C4—24no—
791C22⋊C4—22no—
792C22⋊C4—24no—
793C22⋊C4—22no—
794C22⋊C4—42no—
795C22⋊C4—42no—
796C22⋊C4—42no—
797C22⋊C4—42no—
798C42—21no—
799C42—21no—
800C42—42no—
801C23—21no—
802C23—22no—
803C23—21no—
804C23—21no—
805C23—22no—
806C23—21no—
807C23—21no—
808C23—22no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—22no—
817C23—22no—
818C23—48no—
819C23—48no—
820C23—48no—
821C23—48no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—84no—
839C23—84no—
840C23—84no—
841C23—84no—
842C23—84no—
843C23—84no—
844C23—84no—
845C23—84no—
846C23—84no—
847C23—84no—
848C23#120×C4112yes—
849C23AGL(1,ℤ/8)×C4112yes—
850C23C22×D4×C4111yescharacteristic
851Q8—41no—
852Q8—41no—
853Q8—41no—
854Q8—41no—
855D4—28no—
856D4—22no—
857D4—22no—
858D4—22no—
859D4—22no—
860D4—22no—
861D4—22no—
862D4—22no—
863D4—48no—
864D4—48no—
865D4—48no—
866D4—48no—
867D4—48no—
868D4—41no—
869D4—41no—
870D4—41no—
871D4—41no—
872D4—84no—
873D4#121×C4114yes—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—21no—
887C2×C4—21no—
888C2×C4—21no—
889C2×C4—21no—
890C2×C4—48no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4#120×C4112yes—
909C2×C4AGL(1,ℤ/8)×C4112yes—
910C2×C4C22×D4×C4111yescharacteristic
911C2×C4C22×D4×C4111yescharacteristic
912C2×C4C22×D4×C4111yescharacteristic
913C2×C4C2×#41×C4111yescharacteristic
914C2×C4H(5,𝔽2)×C4111yescharacteristic
915C2×C4H(5,𝔽2)×C4111yescharacteristic
916C8—22no—
917C8—41no—
918C8—41no—
919C8—41no—
920C22—22no—
921C22—22no—
922C22—24no—
923C22—22no—
924C22—22no—
925C22—22no—
926C22—22no—
927C22—41no—
928C22—42no—
929C22—41no—
930C22—41no—
931C22—42no—
932C22—41no—
933C22—42no—
934C22—41no—
935C22—42no—
936C22—41no—
937C22—42no—
938C22—41no—
939C22—41no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—816no—
948C22—816no—
949C22—81no—
950C22—81no—
951C22—81no—
952C22—81no—
953C22—81no—
954C22—81no—
955C22—81no—
956C22—81no—
957C22C2×#120×C4111yescharacteristic
958C22D42×C4111yescharacteristic
959C22C41×#54611yescharacteristic
960C22C2×AGL(1,ℤ/8)×C4111yescharacteristic
961C22C2×AGL(1,ℤ/8)×C4111yescharacteristic
962C22C41×#57711yescharacteristic
963C22C41×#57711yescharacteristic
964C4—22no—
965C4—22no—
966C4—41no—
967C4—42no—
968C4—41no—
969C4—42no—
970C4—81no—
971C4—81no—
972C4—81no—
973C4C2×#121×C4111yescharacteristic
974C4C41×#53411yescharacteristic
975C4D42×C4111yescharacteristic
976C4C41×#54611yescharacteristic
977C2—42no—
978C2—42no—
979C2—44no—
980C2—82no—
981C2—82no—
982C2C41×#241011yescharacteristic
983C2C41×#300311yescharacteristic
984C2C41×#300911yescharacteristic
985C2C41×#326511yescharacteristic
986C2C41×#327211yescharacteristic
987C2C41×#331011yescharacteristic
988C2C41×#332411yescharacteristic
subgroupG/H
center, socleC23×C41C22×D4
commutator, Frattini, cosocleC22×C4C24×C41
prime radicalC2×D42×C41C2
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
2. C2×C41×#468C2semidirect
3. C2×C41×#450C2semidirect
4. C2×C41×#450C2semidirect
5. C2×C41×#418C2semidirect
6. C41×#2415C2semidirect
7. C41×#2041C2semidirect
8. C41×#2033C2semidirect
9. C41×#2014C2semidirect
10. C41×#2000C2semidirect
11. C41×#1877C2semidirect
12. C41×#1875C2semidirect
13. C41×#1870C2semidirect
14. C41×#1862C2semidirect
15. C41×#1786C2semidirect
20. C22×SD16×C41C22semidirect
21. C22×SD16×C41C22semidirect
22. C22×M16×C41C22semidirect
26. C2×C22⋊Q8×C41C22semidirect
27. C2×C22⋊Q8×C41C22semidirect
35. C2×#117×C41C22semidirect
39. C2×#107×C41C22semidirect
41. C2×#103×C41C22semidirect
45. C2×#102×C41C22semidirect
46. C2×#102×C41C22semidirect
47. C2×#102×C41C22semidirect
48. C2×#102×C41C22semidirect
49. C2×#102×C41C22semidirect
50. C2×#102×C41C22semidirect
51. C2×C22⋊C8×C41C22semidirect
52. C2×C22⋊C8×C41C22semidirect
53. C2×C22⋊C8×C41C22semidirect
56. C41×#391C22semidirect
58. C41×#389C22semidirect
60. C41×#380C22semidirect
61. C41×#340C22semidirect
62. C41×#340C22semidirect
63. C41×#336C22semidirect
64. C41×#336C22semidirect
160. #102×C41D4semidirect
281. C2×C8×C41C2×D4semidirect
293. C4⋊C4×C41C2×D4semidirect
425. #24448C41direct (N × H)
484. C2×#468C2×C41semidirect
485. C2×#450C2×C41semidirect
486. C2×#450C2×C41semidirect
487. C2×#418C2×C41semidirect
488. #2415C2×C41semidirect
489. #2041C2×C41semidirect
490. #2033C2×C41semidirect
491. #2014C2×C41semidirect
492. #2000C2×C41semidirect
493. #1877C2×C41semidirect
494. #1875C2×C41semidirect
495. #1870C2×C41semidirect
496. #1862C2×C41semidirect
497. #1786C2×C41semidirect
514. C22×SD16C22×C41semidirect
515. C22×SD16C22×C41semidirect
516. C22×M16C22×C41semidirect
520. C2×C22⋊Q8C22×C41semidirect
521. C2×C22⋊Q8C22×C41semidirect
529. C2×#117C22×C41semidirect
533. C2×#107C22×C41semidirect
535. C2×#103C22×C41semidirect
539. C2×#102C22×C41semidirect
540. C2×#102C22×C41semidirect
541. C2×#102C22×C41semidirect
542. C2×#102C22×C41semidirect
543. C2×#102C22×C41semidirect
544. C2×#102C22×C41semidirect
545. C2×C22⋊C8C22×C41semidirect
546. C2×C22⋊C8C22×C41semidirect
547. C2×C22⋊C8C22×C41semidirect
550. #391C22×C41semidirect
552. #389C22×C41semidirect
554. #380C22×C41semidirect
555. #340C22×C41semidirect
556. #340C22×C41semidirect
557. #336C22×C41semidirect
558. #336C22×C41semidirect
559. C41#24448direct (N × H)
655. #102D4×C41semidirect
776. C2×C8C2×D4×C41semidirect
788. C4⋊C4C2×D4×C41semidirect

Maximal subgroups

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

subgroupindex
C2×D42×C412
C2×C41×#4682
C2×C41×#4502
C2×C41×#4182
C41×#24152
C41×#20412
C41×#20332
C41×#20142
C41×#20002
C41×#18772
C41×#18752
C41×#18702
C41×#18622
C41×#17862
#2444841