Finite Group Databasebeta

← C41×#22887 #23799088

Subgroups — C41×#22887 #23799088

Order 10496.

1020 conjugacy classes of subgroups.

The subgroup lattice has 862 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
4C2×C41×#421C211yesmaximal, characteristic, complemented
5C41×#2880C211yesmaximal, characteristic, complemented
6C41×#1974C211yesmaximal, characteristic, complemented
7C41×#1938C211yesmaximal, characteristic, complemented
8C41×#1929C211yesmaximal, characteristic, complemented
9C41×#1897C211yesmaximal, characteristic, complemented
10C41×#1876C211yesmaximal, characteristic, complemented
11C41×#1876C211yesmaximal, characteristic, complemented
12C41×#1866C211yesmaximal, characteristic, complemented
13C41×#1855C211yesmaximal, characteristic, complemented
14C41×#1764C211yesmaximal, characteristic, complemented
15C41×#1750C211yesmaximal, 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
24C2×#117×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
41C41×#421—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×C4×C8×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×C41C2311yescharacteristic
85#135×C41—22no—
86#135×C41—22no—
87#135×C41—41no—
88#135×C41—41no—
89C2×Q16×C41C2×C411yescharacteristic
90C2×Q16×C41C2×C411yescharacteristic
91C2×SD16×C41C2×C411yescharacteristic
92C2×SD16×C41C2×C411yescharacteristic
93C2×SD16×C41C2×C411yescharacteristic
94C2×SD16×C41C2×C411yescharacteristic
95C2×D8×C41C2×C411yescharacteristic
96C2×D8×C41C2×C411yescharacteristic
97#131×C41—22no—
98#131×C41—22no—
99#131×C41—22no—
100#131×C41—41no—
101#131×C41—41no—
102#131×C41—41no—
103C2×M16×C41—21no—
104C2×M16×C41—21no—
105C2×M16×C41—21no—
106C2×M16×C41—21no—
107C2×M16×C41—22no—
108C2×M16×C41—41no—
109C2×M16×C41C2311yescharacteristic
110C2×M16×C41C2311yescharacteristic
111C2×M16×C41C2311yescharacteristic
112C2×M16×C41C2311yescharacteristic
113C22×C8×C41—21no—
114C22×C8×C41—21no—
115C22×C8×C41—21no—
116C22×C8×C41—21no—
117C22×C8×C41C2311yescharacteristic
118C22×C8×C41C2311yescharacteristic
119C22×C8×C41C2311yescharacteristic
120C22×C8×C41C2311yescharacteristic
121#123×C41—21no—
122C22⋊Q8×C41C2×C411yescharacteristic
123C22⋊Q8×C41C2×C411yescharacteristic
124#121×C41C2×C411yescharacteristic
125#121×C41C2×C411yescharacteristic
126#120×C41—21no—
127C4×D4×C41—21no—
128C4×D4×C41—21no—
129#117×C41—22no—
130#117×C41—41no—
131#117×C41C2311yescharacteristic
132C2×C4⋊C4×C41—21no—
133C2×C22⋊C4×C41—21no—
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
147#103×C41C2×C411yescharacteristic
148#103×C41C2×C411yescharacteristic
149#103×C41C2×C411yescharacteristic
150#102×C41C2×C411yescharacteristic
151#102×C41C2×C411yescharacteristic
152#102×C41C2×C411yescharacteristic
153#102×C41C2×C411yescharacteristic
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—
172C4×C8×C41—21no—
173C4×C8×C41—41no—
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×C41C22×C411yescharacteristic
232C22×C4×C41C22×C411yescharacteristic
233C22×C4×C41C2×D411yescharacteristic
234C22×C4×C41C2×D411yescharacteristic
235C22×C4×C41#4111yescharacteristic
236C22×C4×C41C2411yescharacteristic
237Q16×C41—22no—
238Q16×C41—41no—
239SD16×C41—22no—
240SD16×C41—22no—
241SD16×C41—41no—
242SD16×C41—41no—
243D8×C41—22no—
244D8×C41—41no—
245M16×C41—21no—
246M16×C41—21no—
247M16×C41—21no—
248M16×C41—21no—
249M16×C41—21no—
250M16×C41—21no—
251M16×C41—21no—
252M16×C41—42no—
253M16×C41—42no—
254M16×C41—42no—
255M16×C41—42no—
256M16×C41C2×D412yes—
257C2×C8×C41—21no—
258C2×C8×C41—21no—
259C2×C8×C41—21no—
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—42no—
270C2×C8×C41—42no—
271C2×C8×C41—42no—
272C2×C8×C41—42no—
273C2×C8×C41C22×C411yescharacteristic
274C2×C8×C41C22×C411yescharacteristic
275C2×C8×C41C22×C411yescharacteristic
276C2×C8×C41C22×C411yescharacteristic
277C2×C8×C41C2×D411yescharacteristic
278C2×C8×C41C2×D411yescharacteristic
279C2×C8×C41C2×D411yescharacteristic
280C2×C8×C41C2×D411yescharacteristic
281C4⋊C4×C41—21no—
282C4⋊C4×C41—21no—
283C4⋊C4×C41—42no—
284C4⋊C4×C41C22×C411yescharacteristic
285C4⋊C4×C41C22×C411yescharacteristic
286C22⋊C4×C41—21no—
287C22⋊C4×C41—21no—
288C22⋊C4×C41—21no—
289C22⋊C4×C41—21no—
290C22⋊C4×C41—21no—
291C22⋊C4×C41—42no—
292C42×C41—21no—
293C42×C41—21no—
294C42×C41—21no—
295C42×C41—21no—
296C42×C41C2×D412yes—
297C23×C41—21no—
298C23×C41—21no—
299C23×C41—21no—
300C23×C41—21no—
301C23×C41—21no—
302C23×C41—41no—
303C23×C41—41no—
304C23×C41—42no—
305C23×C41—42no—
306C23×C41—81no—
307C23×C41C4×D411yescharacteristic
308C23×C41C4×D411yescharacteristic
309C23×C41C2×#4111yescharacteristic
310Q8×C41—21no—
311Q8×C41—21no—
312Q8×C41—21no—
313Q8×C41—21no—
314Q8×C41—21no—
315Q8×C41—42no—
316Q8×C41C4×D412yes—
317D4×C41—22no—
318D4×C41—22no—
319D4×C41—21no—
320D4×C41—21no—
321D4×C41—21no—
322D4×C41—21no—
323D4×C41—21no—
324D4×C41—42no—
325D4×C41—42no—
326D4×C41—42no—
327D4×C41—42no—
328D4×C41—41no—
329D4×C41—41no—
330D4×C41—41no—
331D4×C41—41no—
332D4×C41—81no—
333D4×C41C4×D412yes—
334C2×C4×C41—21no—
335C2×C4×C41—21no—
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—22no—
343C2×C4×C41—21no—
344C2×C4×C41—22no—
345C2×C4×C41—21no—
346C2×C4×C41—21no—
347C2×C4×C41—21no—
348C2×C4×C41—21no—
349C2×C4×C41—21no—
350C2×C4×C41—21no—
351C2×C4×C41—22no—
352C2×C4×C41—42no—
353C2×C4×C41—42no—
354C2×C4×C41—42no—
355C2×C4×C41—41no—
356C2×C4×C41—41no—
357C2×C4×C41—41no—
358C2×C4×C41—41no—
359C2×C4×C41—41no—
360C2×C4×C41—41no—
361C2×C4×C41—41no—
362C2×C4×C41—41no—
363C2×C4×C41—41no—
364C2×C4×C41C4×D411yescharacteristic
365C2×C4×C41C4×D411yescharacteristic
366C2×C4×C41C23×C411yescharacteristic
367C2×C4×C41C22×D411yescharacteristic
368C2×C4×C41C22×D411yescharacteristic
369C2×C4×C41C2×#4111yescharacteristic
370C2×C4×C41H(5,𝔽2)11yescharacteristic
371C2×C4×C41H(5,𝔽2)11yescharacteristic
372C8×C41—21no—
373C8×C41—21no—
374C8×C41—21no—
375C8×C41—21no—
376C8×C41—21no—
377C8×C41—21no—
378C8×C41—22no—
379C8×C41—21no—
380C8×C41—21no—
381C8×C41—41no—
382C8×C41—41no—
383C8×C41—41no—
384#22887C4111yesmaximal, characteristic, direct product factor, Sylow
385C22×C41—21no—
386C22×C41—21no—
387C22×C41—21no—
388C22×C41—21no—
389C22×C41—22no—
390C22×C41—21no—
391C22×C41—21no—
392C22×C41—21no—
393C22×C41—21no—
394C22×C41—41no—
395C22×C41—41no—
396C22×C41—41no—
397C22×C41—41no—
398C22×C41—41no—
399C22×C41—41no—
400C22×C41—41no—
401C22×C41—41no—
402C22×C41—81no—
403C22×C41—81no—
404C22×C41—84no—
405C22×C41C2×C4×D411yescharacteristic
406C22×C41#54611yescharacteristic
407C22×C41#55111yescharacteristic
408C4×C41—21no—
409C4×C41—21no—
410C4×C41—22no—
411C4×C41—42no—
412C4×C41—41no—
413C4×C41—41no—
414C4×C41—41no—
415C4×C41—41no—
416C4×C41—81no—
417C4×C41C2×C4×D411yescharacteristic
418C4×C41#51811yescharacteristic
419C4×C41D4211yescharacteristic
420C4×C41#54611yescharacteristic
421#3002C2×C4111yescharacteristic
422C2×#444C2×C4111yescharacteristic, complemented
423#2933C2×C4111yescharacteristic, complemented
424C2×#421C2×C4111yescharacteristic, complemented
425#2880C2×C4111yescharacteristic, complemented
426#1974C2×C4111yescharacteristic, complemented
427#1938C2×C4111yescharacteristic, complemented
428#1929C2×C4111yescharacteristic, complemented
429#1897C2×C4111yescharacteristic, complemented
430#1876C2×C4111yescharacteristic, complemented
431#1876C2×C4111yescharacteristic, complemented
432#1866C2×C4111yescharacteristic, complemented
433#1855C2×C4111yescharacteristic, complemented
434#1764C2×C4111yescharacteristic, complemented
435#1750C2×C4111yescharacteristic, complemented
436C2×C41—21no—
437C2×C41—21no—
438C2×C41—41no—
439C2×C41—41no—
440C2×C41—42no—
441C2×C41—81no—
442C2×C41—81no—
443C2×C41#235811yescharacteristic
444C2×C41#295511yescharacteristic
445C2×C41#295711yescharacteristic
446C22×#41C22×C4111yescharacteristic
447C2×#135C22×C4111yescharacteristic
448C2×#135C22×C4111yescharacteristic
449C2×#131C22×C4111yescharacteristic
450C2×#131C22×C4111yescharacteristic
451C2×#131C22×C4111yescharacteristic, complemented
452C22×M16C22×C4111yescharacteristic
453#525C22×C4111yescharacteristic
454C2×#117C22×C4111yescharacteristic
455#452C4×C4111yescharacteristic, complemented
456#452C4×C4111yescharacteristic, complemented
457#451C4×C4111yescharacteristic, complemented
458#450C4×C4111yescharacteristic, complemented
459#449C4×C4111yescharacteristic, complemented
460#449C4×C4111yescharacteristic, complemented
461#448C4×C4111yescharacteristic, complemented
462#447C4×C4111yescharacteristic, complemented
463#444—24no—
464#436—21no—
465#435—21no—
466#435—21no—
467C8×D4—21no—
468C2×#108C22×C4111yescharacteristic, complemented
469C2×#108C22×C4111yescharacteristic, complemented
470#424C22×C4111yescharacteristic, complemented
471#421—24no—
472C2×#104C22×C4111yescharacteristic
473C2×#104C22×C4111yescharacteristic
474C2×#104C22×C4111yescharacteristic
475C2×#104C22×C4111yescharacteristic
476C2×#104C22×C4111yescharacteristic, complemented
477C2×#104C22×C4111yescharacteristic, complemented
478#416C22×C4111yescharacteristic
479#416C22×C4111yescharacteristic
480#408—21no—
481#408—21no—
482#408C22×C4111yescharacteristic
483#408C22×C4111yescharacteristic
484#408C22×C4111yescharacteristic, complemented
485#407—21no—
486#407C22×C4111yescharacteristic
487C2×C22⋊C8—21no—
488C2×C22⋊C8C22×C4111yescharacteristic
489C2×C22⋊C8C22×C4111yescharacteristic
490#405C22×C4111yescharacteristic, complemented
491C2×#97C22×C4111yescharacteristic, complemented
492C2×C4×C8C22×C4111yescharacteristic, complemented
493#341C22×C4111yescharacteristic, complemented
494#341C22×C4111yescharacteristic, complemented
495#339C22×C4111yescharacteristic, complemented
496#339C22×C4111yescharacteristic, complemented
497#336C22×C4111yescharacteristic, complemented
498#336C22×C4111yescharacteristic, complemented
499C41#2288711yescharacteristic, direct product factor, Sylow
500C2×#41—21no—
501C2×#41—21no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41C2×C4×C4111yescharacteristic
507C2×#41C2×C4×C4111yescharacteristic
508C2×#41C23×C4111yescharacteristic
509C2×#41C23×C4111yescharacteristic
510C2×#41C23×C4111yescharacteristic
511C22×Q8C2×C4×C4111yescharacteristic
512C22×D4—21no—
513C22×D4C2×C4×C4111yescharacteristic
514C23×C4—21no—
515C23×C4C23×C4111yescharacteristic
516#135—22no—
517#135—22no—
518#135—41no—
519#135—41no—
520C2×Q16C2×C4×C4111yescharacteristic
521C2×Q16C2×C4×C4111yescharacteristic
522C2×SD16C2×C4×C4111yescharacteristic
523C2×SD16C2×C4×C4111yescharacteristic
524C2×SD16C2×C4×C4111yescharacteristic
525C2×SD16C2×C4×C4111yescharacteristic
526C2×D8C2×C4×C4111yescharacteristic
527C2×D8C2×C4×C4111yescharacteristic
528#131—22no—
529#131—22no—
530#131—22no—
531#131—41no—
532#131—41no—
533#131—41no—
534C2×M16—21no—
535C2×M16—21no—
536C2×M16—21no—
537C2×M16—21no—
538C2×M16—22no—
539C2×M16—41no—
540C2×M16C23×C4111yescharacteristic
541C2×M16C23×C4111yescharacteristic
542C2×M16C23×C4111yescharacteristic
543C2×M16C23×C4111yescharacteristic
544C22×C8—21no—
545C22×C8—21no—
546C22×C8—21no—
547C22×C8—21no—
548C22×C8C23×C4111yescharacteristic
549C22×C8C23×C4111yescharacteristic
550C22×C8C23×C4111yescharacteristic
551C22×C8C23×C4111yescharacteristic
552#123—21no—
553C22⋊Q8C2×C4×C4111yescharacteristic
554C22⋊Q8C2×C4×C4111yescharacteristic
555#121C2×C4×C4111yescharacteristic
556#121C2×C4×C4111yescharacteristic
557#120—21no—
558C4×D4—21no—
559C4×D4—21no—
560#117—22no—
561#117—41no—
562#117C23×C4111yescharacteristic
563C2×C4⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C42C23×C4111yescharacteristic
566C2×C42C23×C4111yescharacteristic
567#108—22no—
568#108—41no—
569C4⋊C8—21no—
570C4⋊C8—21no—
571#104—22no—
572#104—22no—
573#104—22no—
574#104—22no—
575#104—41no—
576#104D4×C4114yescomplemented
577#103C2×C4×C4111yescharacteristic
578#103C2×C4×C4111yescharacteristic
579#103C2×C4×C4111yescharacteristic
580#103C2×C4×C4111yescharacteristic
581#102C2×C4×C4111yescharacteristic
582#102C2×C4×C4111yescharacteristic
583#102C2×C4×C4111yescharacteristic
584#102C2×C4×C4111yescharacteristic
585C22⋊C8—21no—
586C22⋊C8—21no—
587C22⋊C8—21no—
588C22⋊C8—21no—
589C22⋊C8—21no—
590C22⋊C8—21no—
591C22⋊C8—21no—
592C22⋊C8—21no—
593C22⋊C8C2×C4×C4111yescharacteristic
594C22⋊C8C2×C4×C4111yescharacteristic
595C22⋊C8C2×C4×C4111yescharacteristic
596C22⋊C8C2×C4×C4111yescharacteristic
597C22⋊C8D4×C4111yescharacteristic
598C22⋊C8D4×C4111yescharacteristic
599C22⋊C8D4×C4111yescharacteristic
600C22⋊C8D4×C4111yescharacteristic
601#97—21no—
602#97—22no—
603C4×C8—21no—
604C4×C8—41no—
605C24—21no—
606C24#41×C4111yescharacteristic
607#41—21no—
608#41—21no—
609#41—22no—
610#41—22no—
611#41—21no—
612#41—21no—
613#41—21no—
614#41—21no—
615#41—21no—
616#41—21no—
617#41—21no—
618#41—21no—
619#41—42no—
620#41—42no—
621#41—41no—
622#41—41no—
623#41—42no—
624#41—42no—
625#41C2×D4×C4112yes—
626#41#41×C4112yes—
627C2×Q8—21no—
628C2×Q8—22no—
629C2×Q8—41no—
630C2×Q8C22×C4×C4111yescharacteristic
631C2×Q8C22×C4×C4111yescharacteristic
632C2×Q8C22×C4×C4111yescharacteristic
633C2×D4—21no—
634C2×D4—22no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—41no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4C22×C4×C4111yescharacteristic
646C2×D4C22×C4×C4111yescharacteristic
647C2×D4C22×C4×C4111yescharacteristic
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
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—42no—
661C22×C4—42no—
662C22×C4C22×C4×C4111yescharacteristic
663C22×C4C22×C4×C4111yescharacteristic
664C22×C4C2×D4×C4111yescharacteristic
665C22×C4C2×D4×C4111yescharacteristic
666C22×C4#41×C4111yescharacteristic
667C22×C4C24×C4111yescharacteristic
668Q16—22no—
669Q16—41no—
670SD16—22no—
671SD16—22no—
672SD16—41no—
673SD16—41no—
674D8—22no—
675D8—41no—
676M16—21no—
677M16—21no—
678M16—21no—
679M16—21no—
680M16—21no—
681M16—21no—
682M16—21no—
683M16—42no—
684M16—42no—
685M16—42no—
686M16—42no—
687M16C2×D4×C4112yes—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—42no—
701C2×C8—42no—
702C2×C8—42no—
703C2×C8—42no—
704C2×C8C22×C4×C4111yescharacteristic
705C2×C8C22×C4×C4111yescharacteristic
706C2×C8C22×C4×C4111yescharacteristic
707C2×C8C22×C4×C4111yescharacteristic
708C2×C8C2×D4×C4111yescharacteristic
709C2×C8C2×D4×C4111yescharacteristic
710C2×C8C2×D4×C4111yescharacteristic
711C2×C8C2×D4×C4111yescharacteristic
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—42no—
715C4⋊C4C22×C4×C4111yescharacteristic
716C4⋊C4C22×C4×C4111yescharacteristic
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—21no—
721C22⋊C4—21no—
722C22⋊C4—42no—
723C42—21no—
724C42—21no—
725C42—21no—
726C42—21no—
727C42C2×D4×C4112yes—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—41no—
734C23—41no—
735C23—42no—
736C23—42no—
737C23—81no—
738C23C4×D4×C4111yescharacteristic
739C23C4×D4×C4111yescharacteristic
740C23C2×#41×C4111yescharacteristic
741Q8—21no—
742Q8—21no—
743Q8—21no—
744Q8—21no—
745Q8—21no—
746Q8—42no—
747Q8C4×D4×C4112yes—
748D4—22no—
749D4—22no—
750D4—21no—
751D4—21no—
752D4—21no—
753D4—21no—
754D4—21no—
755D4—42no—
756D4—42no—
757D4—42no—
758D4—42no—
759D4—41no—
760D4—41no—
761D4—41no—
762D4—41no—
763D4—81no—
764D4C4×D4×C4112yes—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—22no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4C4×D4×C4111yescharacteristic
796C2×C4C4×D4×C4111yescharacteristic
797C2×C4C23×C4×C4111yescharacteristic
798C2×C4C22×D4×C4111yescharacteristic
799C2×C4C22×D4×C4111yescharacteristic
800C2×C4C2×#41×C4111yescharacteristic
801C2×C4H(5,𝔽2)×C4111yescharacteristic
802C2×C4H(5,𝔽2)×C4111yescharacteristic
803C8—21no—
804C8—21no—
805C8—21no—
806C8—21no—
807C8—21no—
808C8—21no—
809C8—22no—
810C8—21no—
811C8—21no—
812C8—41no—
813C8—41no—
814C8—41no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—22no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—81no—
833C22—81no—
834C22—84no—
835C22C2×C4×D4×C4111yescharacteristic
836C22C41×#54611yescharacteristic
837C22C41×#55111yescharacteristic
838C4—21no—
839C4—21no—
840C4—22no—
841C4—42no—
842C4—41no—
843C4—41no—
844C4—41no—
845C4—41no—
846C4—81no—
847C4C2×C4×D4×C4111yescharacteristic
848C4C41×#51811yescharacteristic
849C4D42×C4111yescharacteristic
850C4C41×#54611yescharacteristic
851C2—21no—
852C2—21no—
853C2—41no—
854C2—41no—
855C2—42no—
856C2—81no—
857C2—81no—
858C2C41×#235811yescharacteristic
859C2C41×#295511yescharacteristic
860C2C41×#295711yescharacteristic
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. C2×C41×#421C2semidirect
5. C41×#2880C2semidirect
6. C41×#1974C2semidirect
7. C41×#1938C2semidirect
8. C41×#1929C2semidirect
9. C41×#1897C2semidirect
10. C41×#1876C2semidirect
11. C41×#1876C2semidirect
12. C41×#1866C2semidirect
13. C41×#1855C2semidirect
14. C41×#1764C2semidirect
15. C41×#1750C2semidirect
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×C4×C8×C41C22semidirect
63. C41×#341C22semidirect
64. C41×#341C22semidirect
65. C41×#339C22semidirect
66. C41×#339C22semidirect
67. C41×#336C22semidirect
68. C41×#336C22semidirect
145. #104×C41D4semidirect
384. #22887C41direct (N × H)
422. C2×#444C2×C41semidirect
423. #2933C2×C41semidirect
424. C2×#421C2×C41semidirect
425. #2880C2×C41semidirect
426. #1974C2×C41semidirect
427. #1938C2×C41semidirect
428. #1929C2×C41semidirect
429. #1897C2×C41semidirect
430. #1876C2×C41semidirect
431. #1876C2×C41semidirect
432. #1866C2×C41semidirect
433. #1855C2×C41semidirect
434. #1764C2×C41semidirect
435. #1750C2×C41semidirect
451. C2×#131C22×C41semidirect
455. #452C4×C41semidirect
456. #452C4×C41semidirect
457. #451C4×C41semidirect
458. #450C4×C41semidirect
459. #449C4×C41semidirect
460. #449C4×C41semidirect
461. #448C4×C41semidirect
462. #447C4×C41semidirect
468. C2×#108C22×C41semidirect
469. C2×#108C22×C41semidirect
470. #424C22×C41semidirect
476. C2×#104C22×C41semidirect
477. C2×#104C22×C41semidirect
484. #408C22×C41semidirect
490. #405C22×C41semidirect
491. C2×#97C22×C41semidirect
492. C2×C4×C8C22×C41semidirect
493. #341C22×C41semidirect
494. #341C22×C41semidirect
495. #339C22×C41semidirect
496. #339C22×C41semidirect
497. #336C22×C41semidirect
498. #336C22×C41semidirect
499. C41#22887direct (N × H)
576. #104D4×C41semidirect

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
C2×C41×#4212
C41×#28802
C41×#19742
C41×#19382
C41×#19292
C41×#18972
C41×#18762
C41×#18662
C41×#18552
C41×#17642
C41×#17502
#2288741