Finite Group Databasebeta

← C41×#24137 #23800338

Subgroups — C41×#24137 #23800338

Order 10496.

1174 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#552C211yesmaximal, characteristic, complemented
2C2×C41×#478C211yesmaximal, characteristic, complemented
3C2×C41×#440C211yesmaximal, characteristic, complemented
4C41×#2537C211yesmaximal, characteristic
5C41×#2036C211yesmaximal, characteristic, complemented
6C41×#2035C211yesmaximal, characteristic, complemented
7C41×#2000C211yesmaximal, characteristic, complemented
8C41×#2000C211yesmaximal, characteristic, complemented
9C41×#1992C211yesmaximal, characteristic, complemented
10C41×#1955C211yesmaximal, characteristic, complemented
11C41×#1875C211yesmaximal, characteristic, complemented
12C41×#1874C211yesmaximal, characteristic, complemented
13C41×#1854C211yesmaximal, characteristic, complemented
14C41×#1852C211yesmaximal, characteristic, complemented
15C41×#1803C211yesmaximal, characteristic, complemented
16C22×SD16×C41C2211yescharacteristic
17C41×#552—24no—
18C41×#552—24no—
19C2×#126×C41—21no—
20C2×#125×C41—21no—
21C2×#125×C41C2211yescharacteristic
22C2×#123×C41—21no—
23C2×C22⋊Q8×C41C2211yescharacteristic
24C2×C22⋊Q8×C41C2211yescharacteristic
25C2×#121×C41—21no—
26C2×#121×C41C2211yescharacteristic
27C2×#121×C41C2211yescharacteristic
28C2×C4×Q8×C41C2211yescharacteristic
29C2×C4×D4×C41C2211yescharacteristic
30C2×C4×D4×C41C2211yescharacteristic
31C2×#117×C41—21no—
32C2×#117×C41C2211yescharacteristic
33C22×C4⋊C4×C41C2211yescharacteristic
34C41×#478—24no—
35C41×#440—24no—
36C2×#107×C41C2211yescharacteristic
37C2×#107×C41C2211yescharacteristic
38C2×#106×C41C2211yescharacteristic
39C2×C4⋊C8×C41C2211yescharacteristic
40C2×#103×C41C2211yescharacteristic
41C2×#103×C41C2211yescharacteristic
42C2×#103×C41C2211yescharacteristic
43C2×#102×C41C2211yescharacteristic
44C2×#102×C41C2211yescharacteristic
45C2×#102×C41C2211yescharacteristic
46C2×C22⋊C8×C41C2211yescharacteristic
47C2×C22⋊C8×C41C2211yescharacteristic
48C2×C22⋊C8×C41C2211yescharacteristic
49C2×C22⋊C8×C41C2211yescharacteristic
50C2×#97×C41C2211yescharacteristic
51C41×#394—21no—
52C41×#394—21no—
53C41×#384C2211yescharacteristic
54C41×#380—21no—
55C41×#380C2211yescharacteristic
56C41×#380C2211yescharacteristic
57C41×#340C2211yescharacteristic
58C41×#340C2211yescharacteristic
59C41×#340C2211yescharacteristic
60C41×#340C2211yescharacteristic
61C41×#340C2211yescharacteristic
62C41×#340C2211yescharacteristic
63C22×Q8×C41C2311yescharacteristic
64C22×D4×C41—21no—
65C22×D4×C41—21no—
66C22×D4×C41D411yescharacteristic
67C22×D4×C41C2311yescharacteristic
68C23×C4×C41—21no—
69C23×C4×C41—21no—
70C23×C4×C41C2311yescharacteristic
71C23×C4×C41C2311yescharacteristic
72C2×SD16×C41—22no—
73C2×SD16×C41—22no—
74C2×SD16×C41—22no—
75C22×C8×C41C2311yescharacteristic
76C22×C8×C41C2311yescharacteristic
77C22×C8×C41C2311yescharacteristic
78C22×C8×C41C2311yescharacteristic
79#126×C41—28no—
80#125×C41—28no—
81#125×C41—22no—
82#125×C41D414yescomplemented
83#123×C41—28no—
84C22⋊Q8×C41—22no—
85C22⋊Q8×C41—22no—
86C22⋊Q8×C41—22no—
87C22⋊Q8×C41—22no—
88#121×C41—22no—
89#121×C41—22no—
90#121×C41—41no—
91#121×C41—41no—
92#121×C41—44no—
93C4×Q8×C41—22no—
94C4×Q8×C41D414yescomplemented
95C4×D4×C41—22no—
96C4×D4×C41—22no—
97C4×D4×C41—22no—
98C4×D4×C41—22no—
99#117×C41—28no—
100#117×C41—22no—
101#117×C41—22no—
102C2×C4⋊C4×C41—21no—
103C2×C4⋊C4×C41—21no—
104C2×C4⋊C4×C41—21no—
105C2×C4⋊C4×C41—21no—
106C2×C4⋊C4×C41—21no—
107C2×C4⋊C4×C41—21no—
108C2×C4⋊C4×C41—22no—
109C2×C4⋊C4×C41—22no—
110C2×C4⋊C4×C41—21no—
111C2×C4⋊C4×C41—21no—
112C2×C4⋊C4×C41D411yescharacteristic
113C2×C4⋊C4×C41C2311yescharacteristic
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#107×C41—22no—
134#106×C41—22no—
135C4⋊C8×C41—22no—
136#103×C41—22no—
137#103×C41—41no—
138#103×C41—41no—
139#102×C41—22no—
140#102×C41—22no—
141#102×C41—22no—
142C22⋊C8×C41—22no—
143C22⋊C8×C41—22no—
144C22⋊C8×C41—41no—
145C22⋊C8×C41—41no—
146#97×C41—22no—
147#95×C41—21no—
148#95×C41—21no—
149C24×C41—21no—
150C24×C41C2×D411yescharacteristic
151C24×C41C2×D411yescharacteristic
152C2×Q8×C41—21no—
153C2×Q8×C41—21no—
154C2×Q8×C41—21no—
155C2×Q8×C41—21no—
156C2×Q8×C41—21no—
157C2×Q8×C41C2×D412yes—
158C2×D4×C41—22no—
159C2×D4×C41—22no—
160C2×D4×C41—21no—
161C2×D4×C41—21no—
162C2×D4×C41—21no—
163C2×D4×C41—21no—
164C2×D4×C41—21no—
165C2×D4×C41—41no—
166C2×D4×C41—42no—
167C2×D4×C41—42no—
168C2×D4×C41—42no—
169C2×D4×C41—42no—
170C2×D4×C41—81no—
171C2×D4×C41—81no—
172C2×D4×C41#4112yes—
173C22×C4×C41—24no—
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—21no—
184C22×C4×C41—21no—
185C22×C4×C41—21no—
186C22×C4×C41—21no—
187C22×C4×C41—21no—
188C22×C4×C41—21no—
189C22×C4×C41—21no—
190C22×C4×C41—21no—
191C22×C4×C41—21no—
192C22×C4×C41—21no—
193C22×C4×C41—42no—
194C22×C4×C41—42no—
195C22×C4×C41—42no—
196C22×C4×C41—42no—
197C22×C4×C41—42no—
198C22×C4×C41C2×D411yescharacteristic
199C22×C4×C41C2×D411yescharacteristic
200C22×C4×C41C2×D411yescharacteristic
201C22×C4×C41C2×D411yescharacteristic
202C22×C4×C41C2411yescharacteristic
203SD16×C41—28no—
204C2×C8×C41—21no—
205C2×C8×C41—21no—
206C2×C8×C41—21no—
207C2×C8×C41—21no—
208C2×C8×C41—21no—
209C2×C8×C41—21no—
210C2×C8×C41—21no—
211C2×C8×C41—21no—
212C2×C8×C41—21no—
213C2×C8×C41—21no—
214C2×C8×C41—21no—
215C2×C8×C41#4112yes—
216C4⋊C4×C41—24no—
217C4⋊C4×C41—24no—
218C4⋊C4×C41—24no—
219C4⋊C4×C41—24no—
220C4⋊C4×C41—24no—
221C4⋊C4×C41—24no—
222C4⋊C4×C41—22no—
223C4⋊C4×C41—21no—
224C4⋊C4×C41—21no—
225C4⋊C4×C41—21no—
226C4⋊C4×C41—21no—
227C4⋊C4×C41—21no—
228C4⋊C4×C41—21no—
229C4⋊C4×C41—21no—
230C4⋊C4×C41—21no—
231C4⋊C4×C41—21no—
232C4⋊C4×C41—42no—
233C4⋊C4×C41—81no—
234C4⋊C4×C41C2×D412yes—
235C4⋊C4×C41C2×D412yes—
236C4⋊C4×C41C2×D412yes—
237C22⋊C4×C41—24no—
238C22⋊C4×C41—24no—
239C22⋊C4×C41—24no—
240C22⋊C4×C41—22no—
241C22⋊C4×C41—22no—
242C22⋊C4×C41—42no—
243C22⋊C4×C41—42no—
244C22⋊C4×C41—42no—
245C22⋊C4×C41—42no—
246C22⋊C4×C41—42no—
247C42×C41—24no—
248C42×C41—24no—
249C42×C41C2×D412yes—
250C42×C41C2×D412yes—
251C23×C41—21no—
252C23×C41—21no—
253C23×C41—21no—
254C23×C41—21no—
255C23×C41—21no—
256C23×C41—21no—
257C23×C41—21no—
258C23×C41—22no—
259C23×C41—21no—
260C23×C41—21no—
261C23×C41—21no—
262C23×C41—21no—
263C23×C41—21no—
264C23×C41—21no—
265C23×C41—41no—
266C23×C41—41no—
267C23×C41—41no—
268C23×C41—41no—
269C23×C41—41no—
270C23×C41—41no—
271C23×C41AGL(1,ℤ/8)12yes—
272C23×C41C22×D411yescharacteristic
273Q8×C41—22no—
274Q8×C41—22no—
275Q8×C41—41no—
276Q8×C41—41no—
277D4×C41—22no—
278D4×C41—22no—
279D4×C41—44no—
280D4×C41—41no—
281D4×C41—41no—
282D4×C41—84no—
283D4×C41—84no—
284C2×C4×C41—21no—
285C2×C4×C41—21no—
286C2×C4×C41—21no—
287C2×C4×C41—21no—
288C2×C4×C41—21no—
289C2×C4×C41—22no—
290C2×C4×C41—22no—
291C2×C4×C41—22no—
292C2×C4×C41—21no—
293C2×C4×C41—22no—
294C2×C4×C41—21no—
295C2×C4×C41—21no—
296C2×C4×C41—21no—
297C2×C4×C41—21no—
298C2×C4×C41—48no—
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—41no—
307C2×C4×C41—41no—
308C2×C4×C41—41no—
309C2×C4×C41—41no—
310C2×C4×C41—41no—
311C2×C4×C41—41no—
312C2×C4×C41—41no—
313C2×C4×C41—41no—
314C2×C4×C41—41no—
315C2×C4×C41—41no—
316C2×C4×C41—41no—
317C2×C4×C41—41no—
318C2×C4×C41—41no—
319C2×C4×C41—41no—
320C2×C4×C41—41no—
321C2×C4×C41—41no—
322C2×C4×C41—41no—
323C2×C4×C41—41no—
324C2×C4×C41—84no—
325C2×C4×C41#12012yes—
326C2×C4×C41#12012yes—
327C2×C4×C41C22×D411yescharacteristic
328C2×C4×C41C22×D411yescharacteristic
329C2×C4×C41C2×#4111yescharacteristic
330C2×C4×C41C2×#4111yescharacteristic
331C2×C4×C41H(5,𝔽2)11yescharacteristic
332C2×C4×C412−1+411yescharacteristic
333C8×C41—22no—
334C8×C41—41no—
335C8×C41—41no—
336C8×C41—41no—
337#24137C4111yesmaximal, characteristic, direct product factor, Sylow
338C22×C41—22no—
339C22×C41—22no—
340C22×C41—22no—
341C22×C41—41no—
342C22×C41—41no—
343C22×C41—41no—
344C22×C41—41no—
345C22×C41—41no—
346C22×C41—41no—
347C22×C41—41no—
348C22×C41—42no—
349C22×C41—41no—
350C22×C41—41no—
351C22×C41—41no—
352C22×C41—42no—
353C22×C41—41no—
354C22×C41—42no—
355C22×C41—81no—
356C22×C41—81no—
357C22×C41—81no—
358C22×C41—81no—
359C22×C41C2×#12011yescharacteristic
360C22×C41#54611yescharacteristic
361C22×C41#54711yescharacteristic
362C22×C41C2×AGL(1,ℤ/8)11yescharacteristic
363C22×C41#57511yescharacteristic
364C22×C41#57711yescharacteristic
365C22×C41#57811yescharacteristic
366C4×C41—22no—
367C4×C41—22no—
368C4×C41—41no—
369C4×C41—41no—
370C4×C41—42no—
371C4×C41—42no—
372C4×C41—42no—
373C4×C41—42no—
374C4×C41—81no—
375C4×C41—81no—
376C4×C41—81no—
377C4×C41#52511yescharacteristic
378C4×C41#53711yescharacteristic
379C4×C41#54811yescharacteristic
380C4×C41#55011yescharacteristic
381C2×#552C2×C4111yescharacteristic, complemented
382C2×#478C2×C4111yescharacteristic, complemented
383C2×#440C2×C4111yescharacteristic, complemented
384#2537C2×C4111yescharacteristic
385#2036C2×C4111yescharacteristic, complemented
386#2035C2×C4111yescharacteristic, complemented
387#2000C2×C4111yescharacteristic, complemented
388#2000C2×C4111yescharacteristic, complemented
389#1992C2×C4111yescharacteristic, complemented
390#1955C2×C4111yescharacteristic, complemented
391#1875C2×C4111yescharacteristic, complemented
392#1874C2×C4111yescharacteristic, complemented
393#1854C2×C4111yescharacteristic, complemented
394#1852C2×C4111yescharacteristic, complemented
395#1803C2×C4111yescharacteristic, complemented
396C2×C41—42no—
397C2×C41—81no—
398C2×C41—82no—
399C2×C41#240711yescharacteristic
400C2×C41#300611yescharacteristic
401C2×C41#301311yescharacteristic
402C2×C41#331011yescharacteristic
403C2×C41#331511yescharacteristic
404C2×C41#334311yescharacteristic
405C2×C41#334811yescharacteristic
406C22×SD16C22×C4111yescharacteristic
407#552—24no—
408#552—24no—
409C2×#126—21no—
410C2×#125—21no—
411C2×#125C22×C4111yescharacteristic
412C2×#123—21no—
413C2×C22⋊Q8C22×C4111yescharacteristic
414C2×C22⋊Q8C22×C4111yescharacteristic
415C2×#121—21no—
416C2×#121C22×C4111yescharacteristic
417C2×#121C22×C4111yescharacteristic
418C2×C4×Q8C22×C4111yescharacteristic
419C2×C4×D4C22×C4111yescharacteristic
420C2×C4×D4C22×C4111yescharacteristic
421C2×#117—21no—
422C2×#117C22×C4111yescharacteristic
423C22×C4⋊C4C22×C4111yescharacteristic
424#478—24no—
425#440—24no—
426C2×#107C22×C4111yescharacteristic
427C2×#107C22×C4111yescharacteristic
428C2×#106C22×C4111yescharacteristic
429C2×C4⋊C8C22×C4111yescharacteristic
430C2×#103C22×C4111yescharacteristic
431C2×#103C22×C4111yescharacteristic
432C2×#103C22×C4111yescharacteristic
433C2×#102C22×C4111yescharacteristic
434C2×#102C22×C4111yescharacteristic
435C2×#102C22×C4111yescharacteristic
436C2×C22⋊C8C22×C4111yescharacteristic
437C2×C22⋊C8C22×C4111yescharacteristic
438C2×C22⋊C8C22×C4111yescharacteristic
439C2×C22⋊C8C22×C4111yescharacteristic
440C2×#97C22×C4111yescharacteristic
441#394—21no—
442#394—21no—
443#384C22×C4111yescharacteristic
444#380—21no—
445#380C22×C4111yescharacteristic
446#380C22×C4111yescharacteristic
447#340C22×C4111yescharacteristic
448#340C22×C4111yescharacteristic
449#340C22×C4111yescharacteristic
450#340C22×C4111yescharacteristic
451#340C22×C4111yescharacteristic
452#340C22×C4111yescharacteristic
453C41#2413711yescharacteristic, direct product factor, Sylow
454C22×Q8C23×C4111yescharacteristic
455C22×D4—21no—
456C22×D4—21no—
457C22×D4D4×C4111yescharacteristic
458C22×D4C23×C4111yescharacteristic
459C23×C4—21no—
460C23×C4—21no—
461C23×C4C23×C4111yescharacteristic
462C23×C4C23×C4111yescharacteristic
463C2×SD16—22no—
464C2×SD16—22no—
465C2×SD16—22no—
466C22×C8C23×C4111yescharacteristic
467C22×C8C23×C4111yescharacteristic
468C22×C8C23×C4111yescharacteristic
469C22×C8C23×C4111yescharacteristic
470#126—28no—
471#125—28no—
472#125—22no—
473#125D4×C4114yescomplemented
474#123—28no—
475C22⋊Q8—22no—
476C22⋊Q8—22no—
477C22⋊Q8—22no—
478C22⋊Q8—22no—
479#121—22no—
480#121—22no—
481#121—41no—
482#121—41no—
483#121—44no—
484C4×Q8—22no—
485C4×Q8D4×C4114yescomplemented
486C4×D4—22no—
487C4×D4—22no—
488C4×D4—22no—
489C4×D4—22no—
490#117—28no—
491#117—22no—
492#117—22no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4D4×C4111yescharacteristic
504C2×C4⋊C4C23×C4111yescharacteristic
505C2×C4⋊C4C23×C4111yescharacteristic
506C2×C4⋊C4C23×C4111yescharacteristic
507C2×C4⋊C4C23×C4111yescharacteristic
508C2×C4⋊C4C23×C4111yescharacteristic
509C2×C4⋊C4C23×C4111yescharacteristic
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4D4×C4111yescharacteristic
519C2×C22⋊C4D4×C4111yescharacteristic
520C2×C42—21no—
521C2×C42—21no—
522C2×C42C23×C4111yescharacteristic
523#107—22no—
524#107—22no—
525#106—22no—
526C4⋊C8—22no—
527#103—22no—
528#103—41no—
529#103—41no—
530#102—22no—
531#102—22no—
532#102—22no—
533C22⋊C8—22no—
534C22⋊C8—22no—
535C22⋊C8—41no—
536C22⋊C8—41no—
537#97—22no—
538#95—21no—
539#95—21no—
540C24—21no—
541C24C2×D4×C4111yescharacteristic
542C24C2×D4×C4111yescharacteristic
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8C2×D4×C4112yes—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—41no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—81no—
562C2×D4—81no—
563C2×D4#41×C4112yes—
564C22×C4—24no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4C2×D4×C4111yescharacteristic
590C22×C4C2×D4×C4111yescharacteristic
591C22×C4C2×D4×C4111yescharacteristic
592C22×C4C2×D4×C4111yescharacteristic
593C22×C4C24×C4111yescharacteristic
594SD16—28no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8#41×C4112yes—
607C4⋊C4—24no—
608C4⋊C4—24no—
609C4⋊C4—24no—
610C4⋊C4—24no—
611C4⋊C4—24no—
612C4⋊C4—24no—
613C4⋊C4—22no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—42no—
624C4⋊C4—81no—
625C4⋊C4C2×D4×C4112yes—
626C4⋊C4C2×D4×C4112yes—
627C4⋊C4C2×D4×C4112yes—
628C22⋊C4—24no—
629C22⋊C4—24no—
630C22⋊C4—24no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C42—24no—
639C42—24no—
640C42C2×D4×C4112yes—
641C42C2×D4×C4112yes—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—22no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23AGL(1,ℤ/8)×C4112yes—
663C23C22×D4×C4111yescharacteristic
664Q8—22no—
665Q8—22no—
666Q8—41no—
667Q8—41no—
668D4—22no—
669D4—22no—
670D4—44no—
671D4—41no—
672D4—41no—
673D4—84no—
674D4—84no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—21no—
684C2×C4—22no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—48no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—84no—
716C2×C4#120×C4112yes—
717C2×C4#120×C4112yes—
718C2×C4C22×D4×C4111yescharacteristic
719C2×C4C22×D4×C4111yescharacteristic
720C2×C4C2×#41×C4111yescharacteristic
721C2×C4C2×#41×C4111yescharacteristic
722C2×C4H(5,𝔽2)×C4111yescharacteristic
723C2×C42−1+4×C4111yescharacteristic
724C8—22no—
725C8—41no—
726C8—41no—
727C8—41no—
728C22—22no—
729C22—22no—
730C22—22no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—42no—
737C22—41no—
738C22—42no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—42no—
743C22—41no—
744C22—41no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22C2×#120×C4111yescharacteristic
750C22C41×#54611yescharacteristic
751C22C41×#54711yescharacteristic
752C22C2×AGL(1,ℤ/8)×C4111yescharacteristic
753C22C41×#57511yescharacteristic
754C22C41×#57711yescharacteristic
755C22C41×#57811yescharacteristic
756C4—22no—
757C4—22no—
758C4—41no—
759C4—41no—
760C4—42no—
761C4—42no—
762C4—42no—
763C4—42no—
764C4—81no—
765C4—81no—
766C4—81no—
767C4C41×#52511yescharacteristic
768C4C41×#53711yescharacteristic
769C4C41×#54811yescharacteristic
770C4C41×#55011yescharacteristic
771C2—42no—
772C2—81no—
773C2—82no—
774C2C41×#240711yescharacteristic
775C2C41×#300611yescharacteristic
776C2C41×#301311yescharacteristic
777C2C41×#331011yescharacteristic
778C2C41×#331511yescharacteristic
779C2C41×#334311yescharacteristic
780C2C41×#334811yescharacteristic
subgroupG/H
center, socleC23×C41C22×D4
commutator, Frattini, cosocleC22×C4C24×C41
prime radicalC41×#2537C2
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×#552C2semidirect
2. C2×C41×#478C2semidirect
3. C2×C41×#440C2semidirect
5. C41×#2036C2semidirect
6. C41×#2035C2semidirect
7. C41×#2000C2semidirect
8. C41×#2000C2semidirect
9. C41×#1992C2semidirect
10. C41×#1955C2semidirect
11. C41×#1875C2semidirect
12. C41×#1874C2semidirect
13. C41×#1854C2semidirect
14. C41×#1852C2semidirect
15. C41×#1803C2semidirect
82. #125×C41D4semidirect
94. C4×Q8×C41D4semidirect
337. #24137C41direct (N × H)
381. C2×#552C2×C41semidirect
382. C2×#478C2×C41semidirect
383. C2×#440C2×C41semidirect
385. #2036C2×C41semidirect
386. #2035C2×C41semidirect
387. #2000C2×C41semidirect
388. #2000C2×C41semidirect
389. #1992C2×C41semidirect
390. #1955C2×C41semidirect
391. #1875C2×C41semidirect
392. #1874C2×C41semidirect
393. #1854C2×C41semidirect
394. #1852C2×C41semidirect
395. #1803C2×C41semidirect
453. C41#24137direct (N × H)
473. #125D4×C41semidirect
485. C4×Q8D4×C41semidirect

Maximal subgroups

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

subgroupindex
C2×C41×#5522
C2×C41×#4782
C2×C41×#4402
C41×#25372
C41×#20362
C41×#20352
C41×#20002
C41×#19922
C41×#19552
C41×#18752
C41×#18742
C41×#18542
C41×#18522
C41×#18032
#2413741