Finite Group Databasebeta

← C41×#22886 #23799087

Subgroups — C41×#22886 #23799087

Order 10496.

1058 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3002C211yesmaximal, characteristic
2C2×C41×#444C211yesmaximal, characteristic, complemented
3C41×#2933C211yesmaximal, characteristic, complemented
4C22×#104×C41C211yesmaximal, characteristic, complemented
5C41×#2880C211yesmaximal, characteristic, complemented
6C41×#1975C211yesmaximal, characteristic, complemented
7C41×#1938C211yesmaximal, characteristic, complemented
8C41×#1929C211yesmaximal, characteristic, complemented
9C41×#1896C211yesmaximal, characteristic, complemented
10C41×#1876C211yesmaximal, characteristic, complemented
11C41×#1876C211yesmaximal, characteristic, complemented
12C41×#1866C211yesmaximal, characteristic, complemented
13C41×#1855C211yesmaximal, characteristic, complemented
14C41×#1765C211yesmaximal, characteristic, complemented
15C41×#1749C211yesmaximal, characteristic, complemented
16C22×#41×C41C2211yescharacteristic
17C2×#135×C41C2211yescharacteristic
18C2×#135×C41C2211yescharacteristic
19C2×#131×C41C2211yescharacteristic
20C2×#131×C41C2211yescharacteristic
21C2×#131×C41C2211yescharacteristic, complemented
22C22×M16×C41C2211yescharacteristic
23C41×#525C2211yescharacteristic
24C22×C42×C41C2211yescharacteristic
25C41×#452C411yescharacteristic, complemented
26C41×#452C411yescharacteristic, complemented
27C41×#451C411yescharacteristic, complemented
28C41×#450C411yescharacteristic, complemented
29C41×#449C411yescharacteristic, complemented
30C41×#449C411yescharacteristic, complemented
31C41×#448C411yescharacteristic, complemented
32C41×#447C411yescharacteristic, complemented
33C41×#444—24no—
34C41×#436—21no—
35C41×#435—21no—
36C41×#435—21no—
37C8×D4×C41—21no—
38C2×#108×C41C2211yescharacteristic, complemented
39C2×#108×C41C2211yescharacteristic, complemented
40C41×#424C2211yescharacteristic, complemented
41C2×#104×C41—24no—
42C2×#104×C41C2211yescharacteristic
43C2×#104×C41C2211yescharacteristic
44C2×#104×C41C2211yescharacteristic
45C2×#104×C41C2211yescharacteristic
46C2×#104×C41C2211yescharacteristic, complemented
47C2×#104×C41C2211yescharacteristic, complemented
48C41×#416C2211yescharacteristic
49C41×#416C2211yescharacteristic
50C41×#408—21no—
51C41×#408—21no—
52C41×#408C2211yescharacteristic
53C41×#408C2211yescharacteristic
54C41×#408C2211yescharacteristic, complemented
55C41×#407—21no—
56C41×#407C2211yescharacteristic
57C2×C22⋊C8×C41—21no—
58C2×C22⋊C8×C41C2211yescharacteristic
59C2×C22⋊C8×C41C2211yescharacteristic
60C41×#405C2211yescharacteristic, complemented
61C2×#97×C41C2211yescharacteristic, complemented
62C2×#97×C41C2211yescharacteristic, complemented
63C41×#341C2211yescharacteristic, complemented
64C41×#341C2211yescharacteristic, complemented
65C41×#339C2211yescharacteristic, complemented
66C41×#339C2211yescharacteristic, complemented
67C41×#336C2211yescharacteristic, complemented
68C41×#336C2211yescharacteristic, complemented
69C2×#41×C41—21no—
70C2×#41×C41—21no—
71C2×#41×C41—22no—
72C2×#41×C41—22no—
73C2×#41×C41—41no—
74C2×#41×C41—41no—
75C2×#41×C41C2×C411yescharacteristic
76C2×#41×C41C2×C411yescharacteristic
77C2×#41×C41C2311yescharacteristic
78C2×#41×C41C2311yescharacteristic
79C2×#41×C41C2311yescharacteristic
80C22×Q8×C41C2×C411yescharacteristic
81C22×D4×C41—21no—
82C22×D4×C41C2×C411yescharacteristic
83C23×C4×C41—21no—
84C23×C4×C41—21no—
85C23×C4×C41C2311yescharacteristic
86#135×C41—22no—
87#135×C41—22no—
88#135×C41—41no—
89#135×C41—41no—
90C2×Q16×C41C2×C411yescharacteristic, complemented
91C2×Q16×C41C2×C411yescharacteristic, complemented
92C2×SD16×C41C2×C411yescharacteristic, complemented
93C2×SD16×C41C2×C411yescharacteristic, complemented
94C2×SD16×C41C2×C411yescharacteristic, complemented
95C2×SD16×C41C2×C411yescharacteristic, complemented
96C2×D8×C41C2×C411yescharacteristic, complemented
97C2×D8×C41C2×C411yescharacteristic, complemented
98#131×C41—22no—
99#131×C41—22no—
100#131×C41—22no—
101#131×C41—41no—
102#131×C41—41no—
103#131×C41—41no—
104C2×M16×C41—21no—
105C2×M16×C41—21no—
106C2×M16×C41—21no—
107C2×M16×C41—21no—
108C2×M16×C41—22no—
109C2×M16×C41—41no—
110C2×M16×C41C2311yescharacteristic
111C2×M16×C41C2311yescharacteristic
112C2×M16×C41C2311yescharacteristic
113C2×M16×C41C2311yescharacteristic
114C22×C8×C41—21no—
115C22×C8×C41—21no—
116C22×C8×C41—21no—
117C22×C8×C41—21no—
118C22×C8×C41C2311yescharacteristic
119C22×C8×C41C2311yescharacteristic
120C22×C8×C41C2311yescharacteristic
121C22×C8×C41C2311yescharacteristic
122#123×C41—21no—
123C22⋊Q8×C41C2×C411yescharacteristic
124C22⋊Q8×C41C2×C411yescharacteristic
125#121×C41C2×C411yescharacteristic
126#121×C41C2×C411yescharacteristic
127#120×C41—21no—
128C4×D4×C41—21no—
129C4×D4×C41—21no—
130#117×C41C2311yescharacteristic
131C2×C42×C41—22no—
132C2×C42×C41—21no—
133C2×C42×C41—41no—
134C2×C42×C41C2311yescharacteristic
135C2×C42×C41C2311yescharacteristic
136#108×C41—22no—
137#108×C41—41no—
138C4⋊C8×C41—21no—
139C4⋊C8×C41—21no—
140#104×C41—22no—
141#104×C41—22no—
142#104×C41—22no—
143#104×C41—22no—
144#104×C41—41no—
145#104×C41D414yescomplemented
146#103×C41C2×C411yescharacteristic, complemented
147#103×C41C2×C411yescharacteristic, complemented
148#103×C41C2×C411yescharacteristic, complemented
149#103×C41C2×C411yescharacteristic, complemented
150#102×C41C2×C411yescharacteristic, complemented
151#102×C41C2×C411yescharacteristic, complemented
152#102×C41C2×C411yescharacteristic, complemented
153#102×C41C2×C411yescharacteristic, complemented
154C22⋊C8×C41—21no—
155C22⋊C8×C41—21no—
156C22⋊C8×C41—21no—
157C22⋊C8×C41—21no—
158C22⋊C8×C41—21no—
159C22⋊C8×C41—21no—
160C22⋊C8×C41—21no—
161C22⋊C8×C41—21no—
162C22⋊C8×C41C2×C411yescharacteristic
163C22⋊C8×C41C2×C411yescharacteristic
164C22⋊C8×C41C2×C411yescharacteristic
165C22⋊C8×C41C2×C411yescharacteristic
166C22⋊C8×C41D411yescharacteristic
167C22⋊C8×C41D411yescharacteristic
168C22⋊C8×C41D411yescharacteristic
169C22⋊C8×C41D411yescharacteristic
170#97×C41—21no—
171#97×C41—22no—
172#97×C41—41no—
173C4×C8×C41—21no—
174C24×C41—21no—
175C24×C41#4111yescharacteristic
176#41×C41—21no—
177#41×C41—21no—
178#41×C41—22no—
179#41×C41—22no—
180#41×C41—21no—
181#41×C41—21no—
182#41×C41—21no—
183#41×C41—21no—
184#41×C41—21no—
185#41×C41—21no—
186#41×C41—21no—
187#41×C41—21no—
188#41×C41—42no—
189#41×C41—42no—
190#41×C41—41no—
191#41×C41—41no—
192#41×C41—42no—
193#41×C41—42no—
194#41×C41C2×D412yes—
195#41×C41#4112yes—
196C2×Q8×C41—21no—
197C2×Q8×C41—22no—
198C2×Q8×C41—41no—
199C2×Q8×C41C22×C411yescharacteristic
200C2×Q8×C41C22×C411yescharacteristic
201C2×Q8×C41C22×C411yescharacteristic
202C2×D4×C41—21no—
203C2×D4×C41—22no—
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—41no—
212C2×D4×C41—42no—
213C2×D4×C41—42no—
214C2×D4×C41C22×C411yescharacteristic
215C2×D4×C41C22×C411yescharacteristic
216C2×D4×C41C22×C411yescharacteristic
217C22×C4×C41—21no—
218C22×C4×C41—21no—
219C22×C4×C41—21no—
220C22×C4×C41—21no—
221C22×C4×C41—21no—
222C22×C4×C41—21no—
223C22×C4×C41—21no—
224C22×C4×C41—21no—
225C22×C4×C41—21no—
226C22×C4×C41—21no—
227C22×C4×C41—21no—
228C22×C4×C41—21no—
229C22×C4×C41—42no—
230C22×C4×C41—42no—
231C22×C4×C41—42no—
232C22×C4×C41—42no—
233C22×C4×C41—42no—
234C22×C4×C41C22×C411yescharacteristic
235C22×C4×C41C22×C411yescharacteristic
236C22×C4×C41C2×D411yescharacteristic
237C22×C4×C41C2×D411yescharacteristic
238C22×C4×C41#4111yescharacteristic
239C22×C4×C41C2411yescharacteristic
240Q16×C41—22no—
241Q16×C41—41no—
242SD16×C41—22no—
243SD16×C41—22no—
244SD16×C41—41no—
245SD16×C41—41no—
246D8×C41—22no—
247D8×C41—41no—
248M16×C41—21no—
249M16×C41—21no—
250M16×C41—21no—
251M16×C41—21no—
252M16×C41—21no—
253M16×C41—21no—
254M16×C41—21no—
255M16×C41—42no—
256M16×C41—42no—
257M16×C41—42no—
258M16×C41—42no—
259M16×C41C2×D412yes—
260C2×C8×C41—21no—
261C2×C8×C41—21no—
262C2×C8×C41—21no—
263C2×C8×C41—21no—
264C2×C8×C41—21no—
265C2×C8×C41—21no—
266C2×C8×C41—21no—
267C2×C8×C41—21no—
268C2×C8×C41—21no—
269C2×C8×C41—21no—
270C2×C8×C41—21no—
271C2×C8×C41—21no—
272C2×C8×C41—42no—
273C2×C8×C41—42no—
274C2×C8×C41—42no—
275C2×C8×C41—42no—
276C2×C8×C41C22×C411yescharacteristic
277C2×C8×C41C22×C411yescharacteristic
278C2×C8×C41C22×C411yescharacteristic
279C2×C8×C41C22×C411yescharacteristic
280C2×C8×C41C2×D411yescharacteristic
281C2×C8×C41C2×D411yescharacteristic
282C2×C8×C41C2×D411yescharacteristic
283C2×C8×C41C2×D411yescharacteristic
284C4⋊C4×C41—21no—
285C4⋊C4×C41—21no—
286C4⋊C4×C41C22×C411yescharacteristic
287C4⋊C4×C41C22×C411yescharacteristic
288C22⋊C4×C41—21no—
289C22⋊C4×C41—21no—
290C22⋊C4×C41—21no—
291C22⋊C4×C41—21no—
292C22⋊C4×C41—21no—
293C42×C41—21no—
294C42×C41—21no—
295C42×C41—21no—
296C42×C41—21no—
297C42×C41—42no—
298C42×C41C2×D412yes—
299C23×C41—21no—
300C23×C41—21no—
301C23×C41—21no—
302C23×C41—22no—
303C23×C41—21no—
304C23×C41—21no—
305C23×C41—41no—
306C23×C41—42no—
307C23×C41—42no—
308C23×C41—81no—
309C23×C41C4×D411yescharacteristic
310C23×C41C4×D411yescharacteristic
311C23×C41C2×#4111yescharacteristic
312Q8×C41—21no—
313Q8×C41—21no—
314Q8×C41—21no—
315Q8×C41—21no—
316Q8×C41—21no—
317Q8×C41—42no—
318Q8×C41C4×D412yes—
319D4×C41—22no—
320D4×C41—22no—
321D4×C41—21no—
322D4×C41—21no—
323D4×C41—21no—
324D4×C41—21no—
325D4×C41—21no—
326D4×C41—42no—
327D4×C41—42no—
328D4×C41—42no—
329D4×C41—41no—
330D4×C41—41no—
331D4×C41—41no—
332D4×C41—41no—
333D4×C41—42no—
334D4×C41—81no—
335D4×C41C4×D412yes—
336C2×C4×C41—21no—
337C2×C4×C41—21no—
338C2×C4×C41—21no—
339C2×C4×C41—21no—
340C2×C4×C41—21no—
341C2×C4×C41—21no—
342C2×C4×C41—21no—
343C2×C4×C41—21no—
344C2×C4×C41—22no—
345C2×C4×C41—21no—
346C2×C4×C41—22no—
347C2×C4×C41—21no—
348C2×C4×C41—21no—
349C2×C4×C41—22no—
350C2×C4×C41—21no—
351C2×C4×C41—21no—
352C2×C4×C41—21no—
353C2×C4×C41—21no—
354C2×C4×C41—22no—
355C2×C4×C41—42no—
356C2×C4×C41—42no—
357C2×C4×C41—42no—
358C2×C4×C41—41no—
359C2×C4×C41—41no—
360C2×C4×C41—41no—
361C2×C4×C41—48no—
362C2×C4×C41—41no—
363C2×C4×C41—41no—
364C2×C4×C41—41no—
365C2×C4×C41—41no—
366C2×C4×C41—41no—
367C2×C4×C41C4×D411yescharacteristic
368C2×C4×C41C4×D411yescharacteristic
369C2×C4×C41C23×C411yescharacteristic
370C2×C4×C41C22×D411yescharacteristic
371C2×C4×C41C22×D411yescharacteristic
372C2×C4×C41C2×#4111yescharacteristic
373C2×C4×C41H(5,𝔽2)11yescharacteristic
374C2×C4×C41H(5,𝔽2)11yescharacteristic
375C8×C41—21no—
376C8×C41—21no—
377C8×C41—21no—
378C8×C41—21no—
379C8×C41—21no—
380C8×C41—21no—
381C8×C41—22no—
382C8×C41—21no—
383C8×C41—21no—
384C8×C41—41no—
385C8×C41—41no—
386C8×C41—41no—
387#22886C4111yesmaximal, characteristic, direct product factor, Sylow
388C22×C41—21no—
389C22×C41—21no—
390C22×C41—21no—
391C22×C41—21no—
392C22×C41—21no—
393C22×C41—22no—
394C22×C41—21no—
395C22×C41—21no—
396C22×C41—42no—
397C22×C41—42no—
398C22×C41—41no—
399C22×C41—41no—
400C22×C41—41no—
401C22×C41—41no—
402C22×C41—41no—
403C22×C41—41no—
404C22×C41—41no—
405C22×C41—41no—
406C22×C41—84no—
407C22×C41#44412yescomplemented
408C22×C41C2×C4×D411yescharacteristic
409C22×C41#54611yescharacteristic
410C22×C41#55111yescharacteristic
411C4×C41—21no—
412C4×C41—21no—
413C4×C41—22no—
414C4×C41—42no—
415C4×C41—42no—
416C4×C41—41no—
417C4×C41—41no—
418C4×C41—41no—
419C4×C41—41no—
420C4×C41C2×C4×D411yescharacteristic
421C4×C41#51811yescharacteristic
422C4×C41D4211yescharacteristic
423C4×C41#54611yescharacteristic
424#3002C2×C4111yescharacteristic
425C2×#444C2×C4111yescharacteristic, complemented
426#2933C2×C4111yescharacteristic, complemented
427C22×#104C2×C4111yescharacteristic, complemented
428#2880C2×C4111yescharacteristic, complemented
429#1975C2×C4111yescharacteristic, complemented
430#1938C2×C4111yescharacteristic, complemented
431#1929C2×C4111yescharacteristic, complemented
432#1896C2×C4111yescharacteristic, complemented
433#1876C2×C4111yescharacteristic, complemented
434#1876C2×C4111yescharacteristic, complemented
435#1866C2×C4111yescharacteristic, complemented
436#1855C2×C4111yescharacteristic, complemented
437#1765C2×C4111yescharacteristic, complemented
438#1749C2×C4111yescharacteristic, complemented
439C2×C41—21no—
440C2×C41—22no—
441C2×C41—21no—
442C2×C41—41no—
443C2×C41—42no—
444C2×C41—81no—
445C2×C41—81no—
446C2×C41#235811yescharacteristic
447C2×C41C2×#44411yescharacteristic
448C2×C41#295611yescharacteristic
449C22×#41C22×C4111yescharacteristic
450C2×#135C22×C4111yescharacteristic
451C2×#135C22×C4111yescharacteristic
452C2×#131C22×C4111yescharacteristic
453C2×#131C22×C4111yescharacteristic
454C2×#131C22×C4111yescharacteristic, complemented
455C22×M16C22×C4111yescharacteristic
456#525C22×C4111yescharacteristic
457C22×C42C22×C4111yescharacteristic
458#452C4×C4111yescharacteristic, complemented
459#452C4×C4111yescharacteristic, complemented
460#451C4×C4111yescharacteristic, complemented
461#450C4×C4111yescharacteristic, complemented
462#449C4×C4111yescharacteristic, complemented
463#449C4×C4111yescharacteristic, complemented
464#448C4×C4111yescharacteristic, complemented
465#447C4×C4111yescharacteristic, complemented
466#444—24no—
467#436—21no—
468#435—21no—
469#435—21no—
470C8×D4—21no—
471C2×#108C22×C4111yescharacteristic, complemented
472C2×#108C22×C4111yescharacteristic, complemented
473#424C22×C4111yescharacteristic, complemented
474C2×#104—24no—
475C2×#104C22×C4111yescharacteristic
476C2×#104C22×C4111yescharacteristic
477C2×#104C22×C4111yescharacteristic
478C2×#104C22×C4111yescharacteristic
479C2×#104C22×C4111yescharacteristic, complemented
480C2×#104C22×C4111yescharacteristic, complemented
481#416C22×C4111yescharacteristic
482#416C22×C4111yescharacteristic
483#408—21no—
484#408—21no—
485#408C22×C4111yescharacteristic
486#408C22×C4111yescharacteristic
487#408C22×C4111yescharacteristic, complemented
488#407—21no—
489#407C22×C4111yescharacteristic
490C2×C22⋊C8—21no—
491C2×C22⋊C8C22×C4111yescharacteristic
492C2×C22⋊C8C22×C4111yescharacteristic
493#405C22×C4111yescharacteristic, complemented
494C2×#97C22×C4111yescharacteristic, complemented
495C2×#97C22×C4111yescharacteristic, complemented
496#341C22×C4111yescharacteristic, complemented
497#341C22×C4111yescharacteristic, complemented
498#339C22×C4111yescharacteristic, complemented
499#339C22×C4111yescharacteristic, complemented
500#336C22×C4111yescharacteristic, complemented
501#336C22×C4111yescharacteristic, complemented
502C41#2288611yescharacteristic, direct product factor, Sylow
503C2×#41—21no—
504C2×#41—21no—
505C2×#41—22no—
506C2×#41—22no—
507C2×#41—41no—
508C2×#41—41no—
509C2×#41C2×C4×C4111yescharacteristic
510C2×#41C2×C4×C4111yescharacteristic
511C2×#41C23×C4111yescharacteristic
512C2×#41C23×C4111yescharacteristic
513C2×#41C23×C4111yescharacteristic
514C22×Q8C2×C4×C4111yescharacteristic
515C22×D4—21no—
516C22×D4C2×C4×C4111yescharacteristic
517C23×C4—21no—
518C23×C4—21no—
519C23×C4C23×C4111yescharacteristic
520#135—22no—
521#135—22no—
522#135—41no—
523#135—41no—
524C2×Q16C2×C4×C4111yescharacteristic, complemented
525C2×Q16C2×C4×C4111yescharacteristic, complemented
526C2×SD16C2×C4×C4111yescharacteristic, complemented
527C2×SD16C2×C4×C4111yescharacteristic, complemented
528C2×SD16C2×C4×C4111yescharacteristic, complemented
529C2×SD16C2×C4×C4111yescharacteristic, complemented
530C2×D8C2×C4×C4111yescharacteristic, complemented
531C2×D8C2×C4×C4111yescharacteristic, complemented
532#131—22no—
533#131—22no—
534#131—22no—
535#131—41no—
536#131—41no—
537#131—41no—
538C2×M16—21no—
539C2×M16—21no—
540C2×M16—21no—
541C2×M16—21no—
542C2×M16—22no—
543C2×M16—41no—
544C2×M16C23×C4111yescharacteristic
545C2×M16C23×C4111yescharacteristic
546C2×M16C23×C4111yescharacteristic
547C2×M16C23×C4111yescharacteristic
548C22×C8—21no—
549C22×C8—21no—
550C22×C8—21no—
551C22×C8—21no—
552C22×C8C23×C4111yescharacteristic
553C22×C8C23×C4111yescharacteristic
554C22×C8C23×C4111yescharacteristic
555C22×C8C23×C4111yescharacteristic
556#123—21no—
557C22⋊Q8C2×C4×C4111yescharacteristic
558C22⋊Q8C2×C4×C4111yescharacteristic
559#121C2×C4×C4111yescharacteristic
560#121C2×C4×C4111yescharacteristic
561#120—21no—
562C4×D4—21no—
563C4×D4—21no—
564#117C23×C4111yescharacteristic
565C2×C42—22no—
566C2×C42—21no—
567C2×C42—41no—
568C2×C42C23×C4111yescharacteristic
569C2×C42C23×C4111yescharacteristic
570#108—22no—
571#108—41no—
572C4⋊C8—21no—
573C4⋊C8—21no—
574#104—22no—
575#104—22no—
576#104—22no—
577#104—22no—
578#104—41no—
579#104D4×C4114yescomplemented
580#103C2×C4×C4111yescharacteristic, complemented
581#103C2×C4×C4111yescharacteristic, complemented
582#103C2×C4×C4111yescharacteristic, complemented
583#103C2×C4×C4111yescharacteristic, complemented
584#102C2×C4×C4111yescharacteristic, complemented
585#102C2×C4×C4111yescharacteristic, complemented
586#102C2×C4×C4111yescharacteristic, complemented
587#102C2×C4×C4111yescharacteristic, complemented
588C22⋊C8—21no—
589C22⋊C8—21no—
590C22⋊C8—21no—
591C22⋊C8—21no—
592C22⋊C8—21no—
593C22⋊C8—21no—
594C22⋊C8—21no—
595C22⋊C8—21no—
596C22⋊C8C2×C4×C4111yescharacteristic
597C22⋊C8C2×C4×C4111yescharacteristic
598C22⋊C8C2×C4×C4111yescharacteristic
599C22⋊C8C2×C4×C4111yescharacteristic
600C22⋊C8D4×C4111yescharacteristic
601C22⋊C8D4×C4111yescharacteristic
602C22⋊C8D4×C4111yescharacteristic
603C22⋊C8D4×C4111yescharacteristic
604#97—21no—
605#97—22no—
606#97—41no—
607C4×C8—21no—
608C24—21no—
609C24#41×C4111yescharacteristic
610#41—21no—
611#41—21no—
612#41—22no—
613#41—22no—
614#41—21no—
615#41—21no—
616#41—21no—
617#41—21no—
618#41—21no—
619#41—21no—
620#41—21no—
621#41—21no—
622#41—42no—
623#41—42no—
624#41—41no—
625#41—41no—
626#41—42no—
627#41—42no—
628#41C2×D4×C4112yes—
629#41#41×C4112yes—
630C2×Q8—21no—
631C2×Q8—22no—
632C2×Q8—41no—
633C2×Q8C22×C4×C4111yescharacteristic
634C2×Q8C22×C4×C4111yescharacteristic
635C2×Q8C22×C4×C4111yescharacteristic
636C2×D4—21no—
637C2×D4—22no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—41no—
646C2×D4—42no—
647C2×D4—42no—
648C2×D4C22×C4×C4111yescharacteristic
649C2×D4C22×C4×C4111yescharacteristic
650C2×D4C22×C4×C4111yescharacteristic
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—42no—
668C22×C4C22×C4×C4111yescharacteristic
669C22×C4C22×C4×C4111yescharacteristic
670C22×C4C2×D4×C4111yescharacteristic
671C22×C4C2×D4×C4111yescharacteristic
672C22×C4#41×C4111yescharacteristic
673C22×C4C24×C4111yescharacteristic
674Q16—22no—
675Q16—41no—
676SD16—22no—
677SD16—22no—
678SD16—41no—
679SD16—41no—
680D8—22no—
681D8—41no—
682M16—21no—
683M16—21no—
684M16—21no—
685M16—21no—
686M16—21no—
687M16—21no—
688M16—21no—
689M16—42no—
690M16—42no—
691M16—42no—
692M16—42no—
693M16C2×D4×C4112yes—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—21no—
703C2×C8—21no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—42no—
707C2×C8—42no—
708C2×C8—42no—
709C2×C8—42no—
710C2×C8C22×C4×C4111yescharacteristic
711C2×C8C22×C4×C4111yescharacteristic
712C2×C8C22×C4×C4111yescharacteristic
713C2×C8C22×C4×C4111yescharacteristic
714C2×C8C2×D4×C4111yescharacteristic
715C2×C8C2×D4×C4111yescharacteristic
716C2×C8C2×D4×C4111yescharacteristic
717C2×C8C2×D4×C4111yescharacteristic
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4C22×C4×C4111yescharacteristic
721C4⋊C4C22×C4×C4111yescharacteristic
722C22⋊C4—21no—
723C22⋊C4—21no—
724C22⋊C4—21no—
725C22⋊C4—21no—
726C22⋊C4—21no—
727C42—21no—
728C42—21no—
729C42—21no—
730C42—21no—
731C42—42no—
732C42C2×D4×C4112yes—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—22no—
737C23—21no—
738C23—21no—
739C23—41no—
740C23—42no—
741C23—42no—
742C23—81no—
743C23C4×D4×C4111yescharacteristic
744C23C4×D4×C4111yescharacteristic
745C23C2×#41×C4111yescharacteristic
746Q8—21no—
747Q8—21no—
748Q8—21no—
749Q8—21no—
750Q8—21no—
751Q8—42no—
752Q8C4×D4×C4112yes—
753D4—22no—
754D4—22no—
755D4—21no—
756D4—21no—
757D4—21no—
758D4—21no—
759D4—21no—
760D4—42no—
761D4—42no—
762D4—42no—
763D4—41no—
764D4—41no—
765D4—41no—
766D4—41no—
767D4—42no—
768D4—81no—
769D4C4×D4×C4112yes—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—22no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—22no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—22no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—48no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4C4×D4×C4111yescharacteristic
802C2×C4C4×D4×C4111yescharacteristic
803C2×C4C23×C4×C4111yescharacteristic
804C2×C4C22×D4×C4111yescharacteristic
805C2×C4C22×D4×C4111yescharacteristic
806C2×C4C2×#41×C4111yescharacteristic
807C2×C4H(5,𝔽2)×C4111yescharacteristic
808C2×C4H(5,𝔽2)×C4111yescharacteristic
809C8—21no—
810C8—21no—
811C8—21no—
812C8—21no—
813C8—21no—
814C8—21no—
815C8—22no—
816C8—21no—
817C8—21no—
818C8—41no—
819C8—41no—
820C8—41no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—22no—
827C22—21no—
828C22—21no—
829C22—42no—
830C22—42no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—84no—
840C22C41×#44412yescomplemented
841C22C2×C4×D4×C4111yescharacteristic
842C22C41×#54611yescharacteristic
843C22C41×#55111yescharacteristic
844C4—21no—
845C4—21no—
846C4—22no—
847C4—42no—
848C4—42no—
849C4—41no—
850C4—41no—
851C4—41no—
852C4—41no—
853C4C2×C4×D4×C4111yescharacteristic
854C4C41×#51811yescharacteristic
855C4D42×C4111yescharacteristic
856C4C41×#54611yescharacteristic
857C2—21no—
858C2—22no—
859C2—21no—
860C2—41no—
861C2—42no—
862C2—81no—
863C2—81no—
864C2C41×#235811yescharacteristic
865C2C2×C41×#44411yescharacteristic
866C2C41×#295611yescharacteristic
subgroupG/H
centerC2×C4×C41C22×D4
commutatorC2×C4C23×C4×C41
Frattini, cosocleC22×C4C24×C41
socleC22×C41C2×C4×D4
prime radicalC41×#3002C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C41 ◁ C2×C22⋊C8×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C41×#444C2semidirect
3. C41×#2933C2semidirect
4. C22×#104×C41C2semidirect
5. C41×#2880C2semidirect
6. C41×#1975C2semidirect
7. C41×#1938C2semidirect
8. C41×#1929C2semidirect
9. C41×#1896C2semidirect
10. C41×#1876C2semidirect
11. C41×#1876C2semidirect
12. C41×#1866C2semidirect
13. C41×#1855C2semidirect
14. C41×#1765C2semidirect
15. C41×#1749C2semidirect
21. C2×#131×C41C22semidirect
25. C41×#452C4semidirect
26. C41×#452C4semidirect
27. C41×#451C4semidirect
28. C41×#450C4semidirect
29. C41×#449C4semidirect
30. C41×#449C4semidirect
31. C41×#448C4semidirect
32. C41×#447C4semidirect
38. C2×#108×C41C22semidirect
39. C2×#108×C41C22semidirect
40. C41×#424C22semidirect
46. C2×#104×C41C22semidirect
47. C2×#104×C41C22semidirect
54. C41×#408C22semidirect
60. C41×#405C22semidirect
61. C2×#97×C41C22semidirect
62. C2×#97×C41C22semidirect
63. C41×#341C22semidirect
64. C41×#341C22semidirect
65. C41×#339C22semidirect
66. C41×#339C22semidirect
67. C41×#336C22semidirect
68. C41×#336C22semidirect
90. C2×Q16×C41C2×C4semidirect
91. C2×Q16×C41C2×C4semidirect
92. C2×SD16×C41C2×C4semidirect
93. C2×SD16×C41C2×C4semidirect
94. C2×SD16×C41C2×C4semidirect
95. C2×SD16×C41C2×C4semidirect
96. C2×D8×C41C2×C4semidirect
97. C2×D8×C41C2×C4semidirect
145. #104×C41D4semidirect
146. #103×C41C2×C4semidirect
147. #103×C41C2×C4semidirect
148. #103×C41C2×C4semidirect
149. #103×C41C2×C4semidirect
150. #102×C41C2×C4semidirect
151. #102×C41C2×C4semidirect
152. #102×C41C2×C4semidirect
153. #102×C41C2×C4semidirect
387. #22886C41direct (N × H)
407. C22×C41#444semidirect
425. C2×#444C2×C41semidirect
426. #2933C2×C41semidirect
427. C22×#104C2×C41semidirect
428. #2880C2×C41semidirect
429. #1975C2×C41semidirect
430. #1938C2×C41semidirect
431. #1929C2×C41semidirect
432. #1896C2×C41semidirect
433. #1876C2×C41semidirect
434. #1876C2×C41semidirect
435. #1866C2×C41semidirect
436. #1855C2×C41semidirect
437. #1765C2×C41semidirect
438. #1749C2×C41semidirect
454. C2×#131C22×C41semidirect
458. #452C4×C41semidirect
459. #452C4×C41semidirect
460. #451C4×C41semidirect
461. #450C4×C41semidirect
462. #449C4×C41semidirect
463. #449C4×C41semidirect
464. #448C4×C41semidirect
465. #447C4×C41semidirect
471. C2×#108C22×C41semidirect
472. C2×#108C22×C41semidirect
473. #424C22×C41semidirect
479. C2×#104C22×C41semidirect
480. C2×#104C22×C41semidirect
487. #408C22×C41semidirect
493. #405C22×C41semidirect
494. C2×#97C22×C41semidirect
495. C2×#97C22×C41semidirect
496. #341C22×C41semidirect
497. #341C22×C41semidirect
498. #339C22×C41semidirect
499. #339C22×C41semidirect
500. #336C22×C41semidirect
501. #336C22×C41semidirect
502. C41#22886direct (N × H)
524. C2×Q16C2×C4×C41semidirect
525. C2×Q16C2×C4×C41semidirect
526. C2×SD16C2×C4×C41semidirect
527. C2×SD16C2×C4×C41semidirect
528. C2×SD16C2×C4×C41semidirect
529. C2×SD16C2×C4×C41semidirect
530. C2×D8C2×C4×C41semidirect
531. C2×D8C2×C4×C41semidirect
579. #104D4×C41semidirect
580. #103C2×C4×C41semidirect
581. #103C2×C4×C41semidirect
582. #103C2×C4×C41semidirect
583. #103C2×C4×C41semidirect
584. #102C2×C4×C41semidirect
585. #102C2×C4×C41semidirect
586. #102C2×C4×C41semidirect
587. #102C2×C4×C41semidirect
840. C22C41×#444semidirect

Maximal subgroups

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

subgroupindex
C41×#30022
C2×C41×#4442
C41×#29332
C22×#104×C412
C41×#28802
C41×#19752
C41×#19382
C41×#19292
C41×#18962
C41×#18762
C41×#18662
C41×#18552
C41×#17652
C41×#17492
#2288641