Finite Group Databasebeta

← C41×#24910 #23801111

Subgroups — C41×#24910 #23801111

Order 10496.

1010 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#448C211yesmaximal, characteristic
2C2×C41×#440C211yesmaximal, characteristic, complemented
3C41×#2422C211yesmaximal, characteristic
4Q8×C22⋊C4×C41C211yesmaximal, characteristic, complemented
5C41×#2095C211yesmaximal, characteristic, complemented
6C41×#2075C211yesmaximal, characteristic, complemented
7C41×#2055C211yesmaximal, characteristic, complemented
8C41×#2033C211yesmaximal, characteristic
9C41×#1935C211yesmaximal, characteristic, complemented
10C41×#1924C211yesmaximal, characteristic, complemented
11C41×#1880C211yesmaximal, characteristic, complemented
12C41×#1877C211yesmaximal, characteristic, complemented
13C41×#1863C211yesmaximal, characteristic, complemented
14C41×#1803C211yesmaximal, characteristic, complemented
15C41×#1787C211yesmaximal, characteristic, complemented
16C23×Q8×C41C2211yescharacteristic
17C22×SD16×C41C2211yescharacteristic
18C22×SD16×C41C2211yescharacteristic
19C2×#123×C41—21no—
20C2×#121×C41C2211yescharacteristic
21C2×C4×Q8×C41C2211yescharacteristic
22C2×C4×Q8×C41C2211yescharacteristic
23C2×C4×D4×C41C2211yescharacteristic
24C41×#448—24no—
25C41×#440—24no—
26C2×#107×C41C2211yescharacteristic
27C2×#107×C41C2211yescharacteristic
28C2×C4⋊C8×C41C2211yescharacteristic
29C2×#103×C41C2211yescharacteristic
30C2×#103×C41C2211yescharacteristic
31C2×#103×C41C2211yescharacteristic
32C2×#103×C41C2211yescharacteristic
33C2×#103×C41C2211yescharacteristic
34C2×#103×C41C2211yescharacteristic
35C2×#102×C41C2211yescharacteristic
36C2×#102×C41C2211yescharacteristic
37C2×C22⋊C8×C41C2211yescharacteristic
38C2×C22⋊C8×C41C2211yescharacteristic
39C2×#97×C41C2211yescharacteristic
40C41×#397—21no—
41C41×#394—21no—
42C41×#391—21no—
43C41×#391—21no—
44C41×#391C2211yescharacteristic
45C41×#391C2211yescharacteristic
46C41×#390C2211yescharacteristic
47C41×#389C2211yescharacteristic
48C41×#385—21no—
49C41×#384C2211yescharacteristic
50C41×#380—21no—
51C41×#380C2211yescharacteristic
52C41×#380C2211yescharacteristic
53C4×C22⋊C4×C41—21no—
54C4×C22⋊C4×C41C2211yescharacteristic
55C41×#340C2211yescharacteristic
56C41×#340C2211yescharacteristic
57C41×#340C2211yescharacteristic
58C41×#340C2211yescharacteristic
59C41×#336C2211yescharacteristic
60C41×#336C2211yescharacteristic
61C22×Q8×C41—22no—
62C22×Q8×C41—22no—
63C22×Q8×C41—21no—
64C22×Q8×C41—22no—
65C22×Q8×C41—22no—
66C22×Q8×C41—41no—
67C22×Q8×C41—41no—
68C22×Q8×C41C2311yescharacteristic
69C22×Q8×C41C2311yescharacteristic
70C22×D4×C41—21no—
71C22×D4×C41C2311yescharacteristic
72C23×C4×C41—21no—
73C23×C4×C41—21no—
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×C41D414yes—
81C22×C8×C41C2311yescharacteristic
82C22×C8×C41C2311yescharacteristic
83C22×C8×C41C2311yescharacteristic
84C22×C8×C41C2311yescharacteristic
85#123×C41—44no—
86#121×C41—22no—
87#121×C41—41no—
88C4×Q8×C41—22no—
89C4×Q8×C41—22no—
90C4×Q8×C41—41no—
91C4×Q8×C41—41no—
92C4×D4×C41—22no—
93C4×D4×C41—41no—
94C2×C4⋊C4×C41—21no—
95C2×C4⋊C4×C41—21no—
96C2×C4⋊C4×C41—21no—
97C2×C4⋊C4×C41—21no—
98C2×C4⋊C4×C41—21no—
99C2×C4⋊C4×C41C2311yescharacteristic
100C2×C4⋊C4×C41C2311yescharacteristic
101C2×C4⋊C4×C41C2311yescharacteristic
102C2×C4⋊C4×C41C2311yescharacteristic
103C2×C4⋊C4×C41C2311yescharacteristic
104C2×C22⋊C4×C41—21no—
105C2×C22⋊C4×C41—21no—
106C2×C22⋊C4×C41—21no—
107C2×C22⋊C4×C41—21no—
108C2×C22⋊C4×C41—21no—
109C2×C22⋊C4×C41—21no—
110C2×C22⋊C4×C41D411yescharacteristic
111C2×C22⋊C4×C41D411yescharacteristic
112C2×C42×C41—21no—
113C2×C42×C41—21no—
114C2×C42×C41C2311yescharacteristic
115C2×C42×C41C2311yescharacteristic
116#107×C41—22no—
117#107×C41—41no—
118C4⋊C8×C41—41no—
119#103×C41—22no—
120#103×C41—22no—
121#103×C41—22no—
122#103×C41—22no—
123#103×C41—22no—
124#103×C41—41no—
125#102×C41—22no—
126#102×C41—41no—
127C22⋊C8×C41—22no—
128C22⋊C8×C41—41no—
129#97×C41—22no—
130#95×C41—21no—
131#95×C41—21no—
132#95×C41—21no—
133#95×C41—21no—
134#95×C41—21no—
135#95×C41—21no—
136#95×C41—21no—
137#95×C41D411yescharacteristic
138#95×C41D411yescharacteristic
139C24×C41—21no—
140C24×C41C2×D411yescharacteristic
141C2×Q8×C41—24no—
142C2×Q8×C41—21no—
143C2×Q8×C41—21no—
144C2×Q8×C41—21no—
145C2×Q8×C41—21no—
146C2×Q8×C41—21no—
147C2×Q8×C41—21no—
148C2×Q8×C41—21no—
149C2×Q8×C41—21no—
150C2×Q8×C41—42no—
151C2×Q8×C41—42no—
152C2×Q8×C41—44no—
153C2×Q8×C41—44no—
154C2×Q8×C41—44no—
155C2×Q8×C41—44no—
156C2×Q8×C41C2×D412yes—
157C2×Q8×C41#4112yes—
158C2×Q8×C41#4112yes—
159C2×Q8×C41#4112yes—
160C2×D4×C41—21no—
161C2×D4×C41—21no—
162C2×D4×C41—21no—
163C2×D4×C41—21no—
164C2×D4×C41—21no—
165C2×D4×C41—42no—
166C2×D4×C41—42no—
167C2×D4×C41—81no—
168C2×D4×C41C2×D412yes—
169C22×C4×C41—21no—
170C22×C4×C41—24no—
171C22×C4×C41—21no—
172C22×C4×C41—21no—
173C22×C4×C41—21no—
174C22×C4×C41—21no—
175C22×C4×C41—21no—
176C22×C4×C41—21no—
177C22×C4×C41—21no—
178C22×C4×C41—21no—
179C22×C4×C41—21no—
180C22×C4×C41—21no—
181C22×C4×C41—21no—
182C22×C4×C41—21no—
183C22×C4×C41—42no—
184C22×C4×C41—42no—
185C22×C4×C41—42no—
186C22×C4×C41—42no—
187C22×C4×C41—81no—
188C22×C4×C41C2×D411yescharacteristic
189C22×C4×C41C2×D411yescharacteristic
190C22×C4×C41C2×D411yescharacteristic
191C22×C4×C41C2×D411yescharacteristic
192C22×C4×C41C2×D411yescharacteristic
193C22×C4×C41C2411yescharacteristic
194SD16×C41—28no—
195SD16×C41—44no—
196C2×C8×C41—21no—
197C2×C8×C41—21no—
198C2×C8×C41—21no—
199C2×C8×C41—21no—
200C2×C8×C41—21no—
201C2×C8×C41—21no—
202C2×C8×C41—21no—
203C2×C8×C41—21no—
204C2×C8×C41—21no—
205C2×C8×C41—21no—
206C2×C8×C41—21no—
207C2×C8×C41C2×D412yes—
208C4⋊C4×C41—21no—
209C4⋊C4×C41—21no—
210C4⋊C4×C41—21no—
211C4⋊C4×C41—21no—
212C4⋊C4×C41—21no—
213C4⋊C4×C41—21no—
214C4⋊C4×C41—21no—
215C4⋊C4×C41—21no—
216C4⋊C4×C41—21no—
217C4⋊C4×C41—21no—
218C4⋊C4×C41—42no—
219C4⋊C4×C41—42no—
220C4⋊C4×C41—42no—
221C4⋊C4×C41—42no—
222C4⋊C4×C41—81no—
223C22⋊C4×C41—22no—
224C22⋊C4×C41—22no—
225C22⋊C4×C41—42no—
226C22⋊C4×C41—42no—
227C22⋊C4×C41—42no—
228C22⋊C4×C41—42no—
229C22⋊C4×C41—42no—
230C22⋊C4×C41—42no—
231C42×C41—21no—
232C42×C41—21no—
233C42×C41—21no—
234C42×C41—21no—
235C42×C41—42no—
236C42×C41—42no—
237C23×C41—21no—
238C23×C41—21no—
239C23×C41—21no—
240C23×C41—21no—
241C23×C41—21no—
242C23×C41—21no—
243C23×C41—22no—
244C23×C41—41no—
245C23×C41—41no—
246C23×C41—41no—
247C23×C41—41no—
248C23×C41—41no—
249C23×C41—41no—
250C23×C41AGL(1,ℤ/8)12yes—
251C23×C41C22×D411yescharacteristic
252Q8×C41—22no—
253Q8×C41—22no—
254Q8×C41—22no—
255Q8×C41—22no—
256Q8×C41—22no—
257Q8×C41—48no—
258Q8×C41—41no—
259Q8×C41—41no—
260Q8×C41#12314yescomplemented
261D4×C41—22no—
262D4×C41—22no—
263D4×C41—41no—
264D4×C41—41no—
265D4×C41—84no—
266C2×C4×C41—22no—
267C2×C4×C41—22no—
268C2×C4×C41—21no—
269C2×C4×C41—22no—
270C2×C4×C41—21no—
271C2×C4×C41—22no—
272C2×C4×C41—21no—
273C2×C4×C41—21no—
274C2×C4×C41—21no—
275C2×C4×C41—21no—
276C2×C4×C41—21no—
277C2×C4×C41—21no—
278C2×C4×C41—21no—
279C2×C4×C41—21no—
280C2×C4×C41—21no—
281C2×C4×C41—21no—
282C2×C4×C41—21no—
283C2×C4×C41—21no—
284C2×C4×C41—48no—
285C2×C4×C41—41no—
286C2×C4×C41—41no—
287C2×C4×C41—41no—
288C2×C4×C41—41no—
289C2×C4×C41—41no—
290C2×C4×C41—41no—
291C2×C4×C41—41no—
292C2×C4×C41—41no—
293C2×C4×C41—41no—
294C2×C4×C41—41no—
295C2×C4×C41—41no—
296C2×C4×C41—41no—
297C2×C4×C41—41no—
298C2×C4×C41—41no—
299C2×C4×C41—41no—
300C2×C4×C41—41no—
301C2×C4×C41—41no—
302C2×C4×C41—41no—
303C2×C4×C41—41no—
304C2×C4×C41—41no—
305C2×C4×C41—41no—
306C2×C4×C41—84no—
307C2×C4×C41#13712yes—
308C2×C4×C41C22×D411yescharacteristic
309C2×C4×C41C2×#4111yescharacteristic
310C2×C4×C41C2×#4111yescharacteristic
311C2×C4×C41C2×#4111yescharacteristic
312C2×C4×C41H(5,𝔽2)11yescharacteristic
313C2×C4×C41H(5,𝔽2)11yescharacteristic
314C8×C41—22no—
315C8×C41—41no—
316C8×C41—41no—
317C8×C41—41no—
318#24910C4111yesmaximal, characteristic, direct product factor, Sylow
319C22×C41—22no—
320C22×C41—22no—
321C22×C41—22no—
322C22×C41—41no—
323C22×C41—41no—
324C22×C41—41no—
325C22×C41—41no—
326C22×C41—42no—
327C22×C41—42no—
328C22×C41—42no—
329C22×C41—81no—
330C22×C41—81no—
331C22×C41—81no—
332C22×C41—81no—
333C22×C41#52511yescharacteristic
334C22×C41D4211yescharacteristic
335C22×C41#54611yescharacteristic
336C22×C41C2×AGL(1,ℤ/8)11yescharacteristic
337C22×C41C2×#13711yescharacteristic
338C22×C41#57711yescharacteristic
339C22×C41#57811yescharacteristic
340C4×C41—24no—
341C4×C41—22no—
342C4×C41—41no—
343C4×C41—42no—
344C4×C41—41no—
345C4×C41—41no—
346C4×C41—41no—
347C4×C41—81no—
348C4×C41—81no—
349C4×C41—81no—
350C4×C41—81no—
351C4×C41—81no—
352C4×C41C2×#12311yescharacteristic
353C4×C41#53811yescharacteristic
354C4×C41#54611yescharacteristic
355C4×C41#55111yescharacteristic
356C2×#448C2×C4111yescharacteristic
357C2×#440C2×C4111yescharacteristic, complemented
358#2422C2×C4111yescharacteristic
359Q8×C22⋊C4C2×C4111yescharacteristic, complemented
360#2095C2×C4111yescharacteristic, complemented
361#2075C2×C4111yescharacteristic, complemented
362#2055C2×C4111yescharacteristic, complemented
363#2033C2×C4111yescharacteristic
364#1935C2×C4111yescharacteristic, complemented
365#1924C2×C4111yescharacteristic, complemented
366#1880C2×C4111yescharacteristic, complemented
367#1877C2×C4111yescharacteristic, complemented
368#1863C2×C4111yescharacteristic, complemented
369#1803C2×C4111yescharacteristic, complemented
370#1787C2×C4111yescharacteristic, complemented
371C2×C41—42no—
372C2×C41—82no—
373C2×C41#241811yescharacteristic
374C2×C41#311211yescharacteristic
375C2×C41#312111yescharacteristic
376C2×C41#326511yescharacteristic
377C2×C41#327611yescharacteristic
378C2×C41#330811yescharacteristic
379C2×C41#332011yescharacteristic
380C23×Q8C22×C4111yescharacteristic
381C22×SD16C22×C4111yescharacteristic
382C22×SD16C22×C4111yescharacteristic
383C2×#123—21no—
384C2×#121C22×C4111yescharacteristic
385C2×C4×Q8C22×C4111yescharacteristic
386C2×C4×Q8C22×C4111yescharacteristic
387C2×C4×D4C22×C4111yescharacteristic
388#448—24no—
389#440—24no—
390C2×#107C22×C4111yescharacteristic
391C2×#107C22×C4111yescharacteristic
392C2×C4⋊C8C22×C4111yescharacteristic
393C2×#103C22×C4111yescharacteristic
394C2×#103C22×C4111yescharacteristic
395C2×#103C22×C4111yescharacteristic
396C2×#103C22×C4111yescharacteristic
397C2×#103C22×C4111yescharacteristic
398C2×#103C22×C4111yescharacteristic
399C2×#102C22×C4111yescharacteristic
400C2×#102C22×C4111yescharacteristic
401C2×C22⋊C8C22×C4111yescharacteristic
402C2×C22⋊C8C22×C4111yescharacteristic
403C2×#97C22×C4111yescharacteristic
404#397—21no—
405#394—21no—
406#391—21no—
407#391—21no—
408#391C22×C4111yescharacteristic
409#391C22×C4111yescharacteristic
410#390C22×C4111yescharacteristic
411#389C22×C4111yescharacteristic
412#385—21no—
413#384C22×C4111yescharacteristic
414#380—21no—
415#380C22×C4111yescharacteristic
416#380C22×C4111yescharacteristic
417C4×C22⋊C4—21no—
418C4×C22⋊C4C22×C4111yescharacteristic
419#340C22×C4111yescharacteristic
420#340C22×C4111yescharacteristic
421#340C22×C4111yescharacteristic
422#340C22×C4111yescharacteristic
423#336C22×C4111yescharacteristic
424#336C22×C4111yescharacteristic
425C41#2491011yescharacteristic, direct product factor, Sylow
426C22×Q8—22no—
427C22×Q8—22no—
428C22×Q8—21no—
429C22×Q8—22no—
430C22×Q8—22no—
431C22×Q8—41no—
432C22×Q8—41no—
433C22×Q8C23×C4111yescharacteristic
434C22×Q8C23×C4111yescharacteristic
435C22×D4—21no—
436C22×D4C23×C4111yescharacteristic
437C23×C4—21no—
438C23×C4—21no—
439C23×C4C23×C4111yescharacteristic
440C2×SD16—22no—
441C2×SD16—22no—
442C2×SD16—22no—
443C2×SD16—22no—
444C2×SD16—41no—
445C2×SD16D4×C4114yes—
446C22×C8C23×C4111yescharacteristic
447C22×C8C23×C4111yescharacteristic
448C22×C8C23×C4111yescharacteristic
449C22×C8C23×C4111yescharacteristic
450#123—44no—
451#121—22no—
452#121—41no—
453C4×Q8—22no—
454C4×Q8—22no—
455C4×Q8—41no—
456C4×Q8—41no—
457C4×D4—22no—
458C4×D4—41no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4C23×C4111yescharacteristic
465C2×C4⋊C4C23×C4111yescharacteristic
466C2×C4⋊C4C23×C4111yescharacteristic
467C2×C4⋊C4C23×C4111yescharacteristic
468C2×C4⋊C4C23×C4111yescharacteristic
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4D4×C4111yescharacteristic
476C2×C22⋊C4D4×C4111yescharacteristic
477C2×C42—21no—
478C2×C42—21no—
479C2×C42C23×C4111yescharacteristic
480C2×C42C23×C4111yescharacteristic
481#107—22no—
482#107—41no—
483C4⋊C8—41no—
484#103—22no—
485#103—22no—
486#103—22no—
487#103—22no—
488#103—22no—
489#103—41no—
490#102—22no—
491#102—41no—
492C22⋊C8—22no—
493C22⋊C8—41no—
494#97—22no—
495#95—21no—
496#95—21no—
497#95—21no—
498#95—21no—
499#95—21no—
500#95—21no—
501#95—21no—
502#95D4×C4111yescharacteristic
503#95D4×C4111yescharacteristic
504C24—21no—
505C24C2×D4×C4111yescharacteristic
506C2×Q8—24no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—42no—
516C2×Q8—42no—
517C2×Q8—44no—
518C2×Q8—44no—
519C2×Q8—44no—
520C2×Q8—44no—
521C2×Q8C2×D4×C4112yes—
522C2×Q8#41×C4112yes—
523C2×Q8#41×C4112yes—
524C2×Q8#41×C4112yes—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—42no—
531C2×D4—42no—
532C2×D4—81no—
533C2×D4C2×D4×C4112yes—
534C22×C4—21no—
535C22×C4—24no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—81no—
553C22×C4C2×D4×C4111yescharacteristic
554C22×C4C2×D4×C4111yescharacteristic
555C22×C4C2×D4×C4111yescharacteristic
556C22×C4C2×D4×C4111yescharacteristic
557C22×C4C2×D4×C4111yescharacteristic
558C22×C4C24×C4111yescharacteristic
559SD16—28no—
560SD16—44no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8C2×D4×C4112yes—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—42no—
584C4⋊C4—42no—
585C4⋊C4—42no—
586C4⋊C4—42no—
587C4⋊C4—81no—
588C22⋊C4—22no—
589C22⋊C4—22no—
590C22⋊C4—42no—
591C22⋊C4—42no—
592C22⋊C4—42no—
593C22⋊C4—42no—
594C22⋊C4—42no—
595C22⋊C4—42no—
596C42—21no—
597C42—21no—
598C42—21no—
599C42—21no—
600C42—42no—
601C42—42no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—22no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23AGL(1,ℤ/8)×C4112yes—
616C23C22×D4×C4111yescharacteristic
617Q8—22no—
618Q8—22no—
619Q8—22no—
620Q8—22no—
621Q8—22no—
622Q8—48no—
623Q8—41no—
624Q8—41no—
625Q8#123×C4114yescomplemented
626D4—22no—
627D4—22no—
628D4—41no—
629D4—41no—
630D4—84no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—21no—
634C2×C4—22no—
635C2×C4—21no—
636C2×C4—22no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—48no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—84no—
672C2×C4#137×C4112yes—
673C2×C4C22×D4×C4111yescharacteristic
674C2×C4C2×#41×C4111yescharacteristic
675C2×C4C2×#41×C4111yescharacteristic
676C2×C4C2×#41×C4111yescharacteristic
677C2×C4H(5,𝔽2)×C4111yescharacteristic
678C2×C4H(5,𝔽2)×C4111yescharacteristic
679C8—22no—
680C8—41no—
681C8—41no—
682C8—41no—
683C22—22no—
684C22—22no—
685C22—22no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22—42no—
691C22—42no—
692C22—42no—
693C22—81no—
694C22—81no—
695C22—81no—
696C22—81no—
697C22C41×#52511yescharacteristic
698C22D42×C4111yescharacteristic
699C22C41×#54611yescharacteristic
700C22C2×AGL(1,ℤ/8)×C4111yescharacteristic
701C22C2×#137×C4111yescharacteristic
702C22C41×#57711yescharacteristic
703C22C41×#57811yescharacteristic
704C4—22no—
705C4—24no—
706C4—41no—
707C4—41no—
708C4—42no—
709C4—41no—
710C4—41no—
711C4—81no—
712C4—81no—
713C4—81no—
714C4—81no—
715C4—81no—
716C4C2×#123×C4111yescharacteristic
717C4C41×#53811yescharacteristic
718C4C41×#54611yescharacteristic
719C4C41×#55111yescharacteristic
720C2—42no—
721C2—82no—
722C2C41×#241811yescharacteristic
723C2C41×#311211yescharacteristic
724C2C41×#312111yescharacteristic
725C2C41×#326511yescharacteristic
726C2C41×#327611yescharacteristic
727C2C41×#330811yescharacteristic
728C2C41×#332011yescharacteristic
subgroupG/H
center, socleC23×C41C22×D4
commutator, Frattini, cosocleC22×C4C24×C41
prime radicalC2×#121×C41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C41 ◁ C4×C22⋊C4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C41×#440C2semidirect
4. Q8×C22⋊C4×C41C2semidirect
5. C41×#2095C2semidirect
6. C41×#2075C2semidirect
7. C41×#2055C2semidirect
9. C41×#1935C2semidirect
10. C41×#1924C2semidirect
11. C41×#1880C2semidirect
12. C41×#1877C2semidirect
13. C41×#1863C2semidirect
14. C41×#1803C2semidirect
15. C41×#1787C2semidirect
260. Q8×C41#123semidirect
318. #24910C41direct (N × H)
357. C2×#440C2×C41semidirect
359. Q8×C22⋊C4C2×C41semidirect
360. #2095C2×C41semidirect
361. #2075C2×C41semidirect
362. #2055C2×C41semidirect
364. #1935C2×C41semidirect
365. #1924C2×C41semidirect
366. #1880C2×C41semidirect
367. #1877C2×C41semidirect
368. #1863C2×C41semidirect
369. #1803C2×C41semidirect
370. #1787C2×C41semidirect
425. C41#24910direct (N × H)
625. Q8#123×C41semidirect

Maximal subgroups

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

subgroupindex
C2×C41×#4482
C2×C41×#4402
C41×#24222
Q8×C22⋊C4×C412
C41×#20952
C41×#20752
C41×#20552
C41×#20332
C41×#19352
C41×#19242
C41×#18802
C41×#18772
C41×#18632
C41×#18032
C41×#17872
#2491041