Finite Group Databasebeta

← C41×#14405 #23790606

Subgroups — C41×#14405 #23790606

Order 10496.

1750 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#389C211yesmaximal, characteristic, complemented
2C2×C41×#388C211yesmaximal, characteristic
3C2×C41×#388C211yesmaximal, characteristic
4C2×C41×#385C211yesmaximal, characteristic
5C2×C41×#385C211yesmaximal, characteristic
6C2×C41×#385C211yesmaximal, characteristic
7C2×C41×#384C211yesmaximal, characteristic, complemented
8C41×#1444C211yesmaximal, characteristic, complemented
9C41×#1444C211yesmaximal, characteristic, complemented
10C41×#1442C211yesmaximal, characteristic, complemented
11C41×#1441C211yesmaximal, characteristic, complemented
12C41×#1439C211yesmaximal, characteristic
13C41×#1439C211yesmaximal, characteristic
14C41×#1436C211yesmaximal, characteristic, complemented
15C41×#1434C211yesmaximal, characteristic, complemented
16C24×C4×C41C2211yescharacteristic
17C22×C4⋊C4×C41C2211yescharacteristic
18C22×C4⋊C4×C41C2211yescharacteristic
19C22×C4⋊C4×C41C2211yescharacteristic
20C22×C4⋊C4×C41C2211yescharacteristic
21C22×C4⋊C4×C41C2211yescharacteristic
22C22×C4⋊C4×C41C2211yescharacteristic
23C22×C4⋊C4×C41C2211yescharacteristic
24C22×C4⋊C4×C41C2211yescharacteristic
25C22×C4⋊C4×C41C2211yescharacteristic
26C22×C4⋊C4×C41C2211yescharacteristic
27C22×C22⋊C4×C41C2211yescharacteristic
28C22×C22⋊C4×C41C2211yescharacteristic
29C22×C22⋊C4×C41C2211yescharacteristic
30C22×C22⋊C4×C41C2211yescharacteristic
31C22×C22⋊C4×C41C2211yescharacteristic
32C22×C22⋊C4×C41C2211yescharacteristic
33C22×C42×C41C2211yescharacteristic
34C22×C42×C41C2211yescharacteristic
35C41×#389—24no—
36C41×#388—24no—
37C41×#388C418yescomplemented
38C41×#385—24no—
39C41×#385—24no—
40C41×#385—24no—
41C41×#384—24no—
42C2×#95×C41C2211yescharacteristic
43C2×#95×C41C2211yescharacteristic
44C2×#95×C41C2211yescharacteristic
45C2×#95×C41C2211yescharacteristic
46C2×#95×C41C2211yescharacteristic
47C2×#95×C41C2211yescharacteristic
48C2×#95×C41C2211yescharacteristic
49C2×#95×C41C2211yescharacteristic
50C2×#95×C41C2211yescharacteristic
51C2×#95×C41C2211yescharacteristic
52C2×#95×C41C2211yescharacteristic
53C2×#95×C41C2211yescharacteristic
54C2×#95×C41C2211yescharacteristic
55C2×#95×C41C2211yescharacteristic
56C2×#95×C41C2211yescharacteristic
57C2×#95×C41C2211yescharacteristic
58C25×C41C2311yescharacteristic
59C23×C4×C41—22no—
60C23×C4×C41—22no—
61C23×C4×C41—22no—
62C23×C4×C41—41no—
63C23×C4×C41—41no—
64C23×C4×C41—41no—
65C23×C4×C41—41no—
66C23×C4×C41C2311yescharacteristic
67C23×C4×C41C2311yescharacteristic
68C23×C4×C41C2311yescharacteristic
69C23×C4×C41C2311yescharacteristic
70C23×C4×C41C2311yescharacteristic
71C23×C4×C41C2311yescharacteristic
72C23×C4×C41C2311yescharacteristic
73C23×C4×C41C2311yescharacteristic
74C23×C4×C41C2311yescharacteristic
75C23×C4×C41C2311yescharacteristic
76C23×C4×C41C2311yescharacteristic
77C23×C4×C41C2311yescharacteristic
78C23×C4×C41C2311yescharacteristic
79C23×C4×C41C2311yescharacteristic
80C2×C4⋊C4×C41—22no—
81C2×C4⋊C4×C41—22no—
82C2×C4⋊C4×C41—22no—
83C2×C4⋊C4×C41—22no—
84C2×C4⋊C4×C41—22no—
85C2×C4⋊C4×C41—22no—
86C2×C4⋊C4×C41—22no—
87C2×C4⋊C4×C41—22no—
88C2×C4⋊C4×C41—22no—
89C2×C4⋊C4×C41—22no—
90C2×C4⋊C4×C41—22no—
91C2×C4⋊C4×C41—22no—
92C2×C4⋊C4×C41—22no—
93C2×C4⋊C4×C41—22no—
94C2×C4⋊C4×C41—22no—
95C2×C4⋊C4×C41—22no—
96C2×C4⋊C4×C41—41no—
97C2×C4⋊C4×C41—41no—
98C2×C4⋊C4×C41—41no—
99C2×C4⋊C4×C41—41no—
100C2×C4⋊C4×C41—41no—
101C2×C4⋊C4×C41—41no—
102C2×C4⋊C4×C41—41no—
103C2×C4⋊C4×C41—41no—
104C2×C4⋊C4×C41—41no—
105C2×C4⋊C4×C41—41no—
106C2×C4⋊C4×C41—41no—
107C2×C4⋊C4×C41—41no—
108C2×C4⋊C4×C41C2×C414yescomplemented
109C2×C4⋊C4×C41D414yes—
110C2×C22⋊C4×C41—22no—
111C2×C22⋊C4×C41—22no—
112C2×C22⋊C4×C41—22no—
113C2×C22⋊C4×C41—22no—
114C2×C22⋊C4×C41—22no—
115C2×C22⋊C4×C41—22no—
116C2×C22⋊C4×C41—22no—
117C2×C22⋊C4×C41—22no—
118C2×C22⋊C4×C41—22no—
119C2×C22⋊C4×C41—41no—
120C2×C22⋊C4×C41—41no—
121C2×C22⋊C4×C41—41no—
122C2×C22⋊C4×C41—41no—
123C2×C22⋊C4×C41C2×C414yes—
124C2×C22⋊C4×C41C2×C414yes—
125C2×C22⋊C4×C41C2×C414yes—
126C2×C22⋊C4×C41D414yes—
127C2×C22⋊C4×C41Q814yes—
128C2×C42×C41—22no—
129C2×C42×C41—22no—
130C2×C42×C41—22no—
131C2×C42×C41—22no—
132C2×C42×C41—41no—
133C2×C42×C41C2×C414yescomplemented
134#95×C41—22no—
135#95×C41—22no—
136#95×C41—22no—
137#95×C41—22no—
138#95×C41—22no—
139#95×C41—22no—
140#95×C41—22no—
141#95×C41—22no—
142#95×C41—22no—
143#95×C41—22no—
144#95×C41—41no—
145#95×C41—41no—
146#95×C41—41no—
147#95×C41C2×C414yescomplemented
148#95×C41C2×C414yescomplemented
149#95×C41D414yes—
150C24×C41—21no—
151C24×C41—21no—
152C24×C41—21no—
153C24×C41—21no—
154C24×C41—21no—
155C24×C41—21no—
156C24×C41—21no—
157C24×C41—21no—
158C24×C41—21no—
159C24×C41—21no—
160C24×C41—21no—
161C24×C41—21no—
162C24×C41C22×C412yes—
163C24×C41C2×D412yes—
164C24×C41C2×Q812yes—
165C24×C41C2411yescharacteristic
166C22×C4×C41—21no—
167C22×C4×C41—21no—
168C22×C4×C41—21no—
169C22×C4×C41—21no—
170C22×C4×C41—21no—
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—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—21no—
194C22×C4×C41—21no—
195C22×C4×C41—21no—
196C22×C4×C41—21no—
197C22×C4×C41—21no—
198C22×C4×C41—21no—
199C22×C4×C41—21no—
200C22×C4×C41—21no—
201C22×C4×C41—21no—
202C22×C4×C41—21no—
203C22×C4×C41—21no—
204C22×C4×C41—21no—
205C22×C4×C41—21no—
206C22×C4×C41—21no—
207C22×C4×C41—21no—
208C22×C4×C41—21no—
209C22×C4×C41—21no—
210C22×C4×C41—21no—
211C22×C4×C41—21no—
212C22×C4×C41—21no—
213C22×C4×C41—21no—
214C22×C4×C41—21no—
215C22×C4×C41—21no—
216C22×C4×C41—21no—
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—21no—
230C22×C4×C41—21no—
231C22×C4×C41—21no—
232C22×C4×C41—21no—
233C22×C4×C41—21no—
234C22×C4×C41—21no—
235C22×C4×C41—21no—
236C22×C4×C41—21no—
237C22×C4×C41—21no—
238C22×C4×C41—21no—
239C22×C4×C41—21no—
240C22×C4×C41—21no—
241C22×C4×C41—21no—
242C22×C4×C41—21no—
243C22×C4×C41—21no—
244C22×C4×C41—21no—
245C22×C4×C41—21no—
246C22×C4×C41—44no—
247C22×C4×C41—44no—
248C22×C4×C41—44no—
249C22×C4×C41—44no—
250C22×C4×C41—44no—
251C22×C4×C41—44no—
252C22×C4×C41—44no—
253C22×C4×C41C22×C412yes—
254C22×C4×C41C22×C412yes—
255C22×C4×C41C22×C412yes—
256C22×C4×C41C22×C412yes—
257C22×C4×C41C22×C412yes—
258C22×C4×C41C22×C412yes—
259C22×C4×C41C2×D412yes—
260C22×C4×C41C2×D412yes—
261C22×C4×C41C2×D412yes—
262C22×C4×C41C2×D412yes—
263C22×C4×C41C2×D412yes—
264C22×C4×C41C2×D412yes—
265C22×C4×C41C2×D412yes—
266C22×C4×C41C2×D412yes—
267C22×C4×C41C2×Q812yes—
268C22×C4×C41C2×Q812yes—
269C22×C4×C41#4112yes—
270C22×C4×C41#4112yes—
271C4⋊C4×C41—28no—
272C4⋊C4×C41—44no—
273C4⋊C4×C41—44no—
274C4⋊C4×C41—44no—
275C4⋊C4×C41—44no—
276C4⋊C4×C41—44no—
277C4⋊C4×C41—44no—
278C4⋊C4×C41—44no—
279C4⋊C4×C41—44no—
280C4⋊C4×C41—44no—
281C22⋊C4×C41—28no—
282C22⋊C4×C41—28no—
283C22⋊C4×C41—44no—
284C22⋊C4×C41—44no—
285C22⋊C4×C41—44no—
286C22⋊C4×C41C4⋊C4116yescomplemented
287C42×C41—28no—
288C42×C41—44no—
289C23×C41—22no—
290C23×C41—22no—
291C23×C41—22no—
292C23×C41—22no—
293C23×C41—22no—
294C23×C41—22no—
295C23×C41—22no—
296C23×C41—22no—
297C23×C41—22no—
298C23×C41—22no—
299C23×C41—22no—
300C23×C41—22no—
301C23×C41—22no—
302C23×C41—22no—
303C23×C41—22no—
304C23×C41—22no—
305C23×C41—22no—
306C23×C41—22no—
307C23×C41—41no—
308C23×C41—41no—
309C23×C41—41no—
310C23×C41—41no—
311C23×C41—41no—
312C23×C41—41no—
313C23×C41—41no—
314C23×C41—41no—
315C23×C41—41no—
316C23×C41—41no—
317C23×C41—41no—
318C23×C41—41no—
319C23×C41—41no—
320C23×C41—41no—
321C23×C41—41no—
322C23×C41—41no—
323C23×C41C2×C4⋊C414yes—
324C23×C41C23×C411yescharacteristic
325C23×C41C22×D411yescharacteristic
326C23×C41C22×D411yescharacteristic
327C23×C41C22×D411yescharacteristic
328C23×C41C22×Q811yescharacteristic
329C23×C41C2×#4111yescharacteristic
330C23×C41C2×#4111yescharacteristic
331C23×C41H(5,𝔽2)11yescharacteristic
332C23×C41H(5,𝔽2)11yescharacteristic
333C23×C41H(5,𝔽2)11yescharacteristic
334C23×C41H(5,𝔽2)11yescharacteristic
335C23×C412−1+411yescharacteristic
336C23×C412−1+411yescharacteristic
337C23×C412−1+411yescharacteristic
338C23×C412−1+411yescharacteristic
339C2×C4×C41—22no—
340C2×C4×C41—22no—
341C2×C4×C41—22no—
342C2×C4×C41—22no—
343C2×C4×C41—22no—
344C2×C4×C41—22no—
345C2×C4×C41—22no—
346C2×C4×C41—22no—
347C2×C4×C41—22no—
348C2×C4×C41—22no—
349C2×C4×C41—22no—
350C2×C4×C41—22no—
351C2×C4×C41—22no—
352C2×C4×C41—22no—
353C2×C4×C41—22no—
354C2×C4×C41—22no—
355C2×C4×C41—22no—
356C2×C4×C41—22no—
357C2×C4×C41—22no—
358C2×C4×C41—22no—
359C2×C4×C41—22no—
360C2×C4×C41—22no—
361C2×C4×C41—22no—
362C2×C4×C41—22no—
363C2×C4×C41—22no—
364C2×C4×C41—22no—
365C2×C4×C41—22no—
366C2×C4×C41—22no—
367C2×C4×C41—22no—
368C2×C4×C41—22no—
369C2×C4×C41—22no—
370C2×C4×C41—22no—
371C2×C4×C41—22no—
372C2×C4×C41—22no—
373C2×C4×C41—22no—
374C2×C4×C41—22no—
375C2×C4×C41—22no—
376C2×C4×C41—22no—
377C2×C4×C41—22no—
378C2×C4×C41—22no—
379C2×C4×C41—22no—
380C2×C4×C41—22no—
381C2×C4×C41—416no—
382C2×C4×C41—41no—
383C2×C4×C41—41no—
384C2×C4×C41—41no—
385C2×C4×C41—41no—
386C2×C4×C41—41no—
387C2×C4×C41—41no—
388C2×C4×C41—41no—
389C2×C4×C41—41no—
390C2×C4×C41—41no—
391C2×C4×C41—41no—
392C2×C4×C41—41no—
393C2×C4×C41—41no—
394C2×C4×C41—41no—
395C2×C4×C41—41no—
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—41no—
414C2×C4×C41—41no—
415C2×C4×C41—41no—
416C2×C4×C41—41no—
417C2×C4×C41—41no—
418C2×C4×C41—41no—
419C2×C4×C41—41no—
420C2×C4×C41—41no—
421C2×C4×C41—41no—
422C2×C4×C41—41no—
423C2×C4×C41—41no—
424C2×C4×C41—41no—
425C2×C4×C41—41no—
426C2×C4×C41—41no—
427C2×C4×C41—41no—
428C2×C4×C41—41no—
429C2×C4×C41—41no—
430C2×C4×C41—41no—
431C2×C4×C41—41no—
432C2×C4×C41—41no—
433C2×C4×C41—41no—
434C2×C4×C41C2×C4⋊C414yes—
435C2×C4×C41C2×C4⋊C414yes—
436C2×C4×C41C4×D414yes—
437C2×C4×C41C4×D414yes—
438#14405C4111yesmaximal, characteristic, direct product factor, Sylow
439C22×C41—24no—
440C22×C41—24no—
441C22×C41—24no—
442C22×C41—42no—
443C22×C41—42no—
444C22×C41—42no—
445C22×C41—42no—
446C22×C41—42no—
447C22×C41—42no—
448C22×C41—42no—
449C22×C41—42no—
450C22×C41—42no—
451C22×C41—42no—
452C22×C41—42no—
453C22×C41—42no—
454C22×C41C22×C4⋊C411yescharacteristic
455C22×C41C2×C4×D411yescharacteristic
456C22×C41C2×C4×D411yescharacteristic
457C22×C41#52011yescharacteristic
458C22×C41#52011yescharacteristic
459C22×C41#52011yescharacteristic
460C22×C41#52011yescharacteristic
461C22×C41#53411yescharacteristic
462C22×C41#53511yescharacteristic
463C22×C41#53511yescharacteristic
464C22×C41#53611yescharacteristic
465C22×C41#53611yescharacteristic
466C22×C41#53611yescharacteristic
467C22×C41#53911yescharacteristic
468C22×C41#53911yescharacteristic
469C22×C41#54211yescharacteristic
470C22×C41#54211yescharacteristic
471C22×C41#54411yescharacteristic
472C22×C41#54411yescharacteristic
473C22×C41D4211yescharacteristic
474C22×C41D4211yescharacteristic
475C22×C41D4211yescharacteristic
476C22×C41#54711yescharacteristic
477C22×C41#54711yescharacteristic
478C22×C41#54711yescharacteristic
479C22×C41#54811yescharacteristic
480C22×C41D4×Q811yescharacteristic
481C22×C41D4×Q811yescharacteristic
482C22×C41#55311yescharacteristic
483C22×C41#55411yescharacteristic
484C22×C41#55411yescharacteristic
485C22×C41#56011yescharacteristic
486C22×C41#56311yescharacteristic
487C22×C41#56311yescharacteristic
488C22×C41#56311yescharacteristic
489C4×C41—24no—
490C4×C41—24no—
491C4×C41—24no—
492C4×C41—24no—
493C4×C41—42no—
494C4×C41—42no—
495C4×C41—42no—
496C4×C41—42no—
497C4×C41—42no—
498C4×C41—42no—
499C4×C41—81no—
500C4×C41—81no—
501C4×C41—81no—
502C4×C41—81no—
503C2×#389C2×C4111yescharacteristic, complemented
504C2×#388C2×C4111yescharacteristic
505C2×#388C2×C4111yescharacteristic
506C2×#385C2×C4111yescharacteristic
507C2×#385C2×C4111yescharacteristic
508C2×#385C2×C4111yescharacteristic
509C2×#384C2×C4111yescharacteristic, complemented
510#1444C2×C4111yescharacteristic, complemented
511#1444C2×C4111yescharacteristic, complemented
512#1442C2×C4111yescharacteristic, complemented
513#1441C2×C4111yescharacteristic, complemented
514#1439C2×C4111yescharacteristic
515#1439C2×C4111yescharacteristic
516#1436C2×C4111yescharacteristic, complemented
517#1434C2×C4111yescharacteristic, complemented
518C2×C41—44no—
519C2×C41#231711yescharacteristic
520C2×C41#232211yescharacteristic
521C2×C41#232611yescharacteristic
522C2×C41D4×C4⋊C411yescharacteristic
523C2×C41D4×C4⋊C411yescharacteristic
524C2×C41#236111yescharacteristic
525C2×C41#238311yescharacteristic
526C2×C41#266911yescharacteristic
527C2×C41#267411yescharacteristic
528C2×C41#267711yescharacteristic
529C2×C41#268011yescharacteristic
530C2×C41#271811yescharacteristic
531C2×C41#272011yescharacteristic
532C2×C41#272911yescharacteristic
533C2×C41#279011yescharacteristic
534C24×C4C22×C4111yescharacteristic
535C22×C4⋊C4C22×C4111yescharacteristic
536C22×C4⋊C4C22×C4111yescharacteristic
537C22×C4⋊C4C22×C4111yescharacteristic
538C22×C4⋊C4C22×C4111yescharacteristic
539C22×C4⋊C4C22×C4111yescharacteristic
540C22×C4⋊C4C22×C4111yescharacteristic
541C22×C4⋊C4C22×C4111yescharacteristic
542C22×C4⋊C4C22×C4111yescharacteristic
543C22×C4⋊C4C22×C4111yescharacteristic
544C22×C4⋊C4C22×C4111yescharacteristic
545C22×C22⋊C4C22×C4111yescharacteristic
546C22×C22⋊C4C22×C4111yescharacteristic
547C22×C22⋊C4C22×C4111yescharacteristic
548C22×C22⋊C4C22×C4111yescharacteristic
549C22×C22⋊C4C22×C4111yescharacteristic
550C22×C22⋊C4C22×C4111yescharacteristic
551C22×C42C22×C4111yescharacteristic
552C22×C42C22×C4111yescharacteristic
553#389—24no—
554#388—24no—
555#388C4×C4118yescomplemented
556#385—24no—
557#385—24no—
558#385—24no—
559#384—24no—
560C2×#95C22×C4111yescharacteristic
561C2×#95C22×C4111yescharacteristic
562C2×#95C22×C4111yescharacteristic
563C2×#95C22×C4111yescharacteristic
564C2×#95C22×C4111yescharacteristic
565C2×#95C22×C4111yescharacteristic
566C2×#95C22×C4111yescharacteristic
567C2×#95C22×C4111yescharacteristic
568C2×#95C22×C4111yescharacteristic
569C2×#95C22×C4111yescharacteristic
570C2×#95C22×C4111yescharacteristic
571C2×#95C22×C4111yescharacteristic
572C2×#95C22×C4111yescharacteristic
573C2×#95C22×C4111yescharacteristic
574C2×#95C22×C4111yescharacteristic
575C2×#95C22×C4111yescharacteristic
576C41#1440511yescharacteristic, direct product factor, Sylow
577C25C23×C4111yescharacteristic
578C23×C4—22no—
579C23×C4—22no—
580C23×C4—22no—
581C23×C4—41no—
582C23×C4—41no—
583C23×C4—41no—
584C23×C4—41no—
585C23×C4C23×C4111yescharacteristic
586C23×C4C23×C4111yescharacteristic
587C23×C4C23×C4111yescharacteristic
588C23×C4C23×C4111yescharacteristic
589C23×C4C23×C4111yescharacteristic
590C23×C4C23×C4111yescharacteristic
591C23×C4C23×C4111yescharacteristic
592C23×C4C23×C4111yescharacteristic
593C23×C4C23×C4111yescharacteristic
594C23×C4C23×C4111yescharacteristic
595C23×C4C23×C4111yescharacteristic
596C23×C4C23×C4111yescharacteristic
597C23×C4C23×C4111yescharacteristic
598C23×C4C23×C4111yescharacteristic
599C2×C4⋊C4—22no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—22no—
602C2×C4⋊C4—22no—
603C2×C4⋊C4—22no—
604C2×C4⋊C4—22no—
605C2×C4⋊C4—22no—
606C2×C4⋊C4—22no—
607C2×C4⋊C4—22no—
608C2×C4⋊C4—22no—
609C2×C4⋊C4—22no—
610C2×C4⋊C4—22no—
611C2×C4⋊C4—22no—
612C2×C4⋊C4—22no—
613C2×C4⋊C4—22no—
614C2×C4⋊C4—22no—
615C2×C4⋊C4—41no—
616C2×C4⋊C4—41no—
617C2×C4⋊C4—41no—
618C2×C4⋊C4—41no—
619C2×C4⋊C4—41no—
620C2×C4⋊C4—41no—
621C2×C4⋊C4—41no—
622C2×C4⋊C4—41no—
623C2×C4⋊C4—41no—
624C2×C4⋊C4—41no—
625C2×C4⋊C4—41no—
626C2×C4⋊C4—41no—
627C2×C4⋊C4C2×C4×C4114yescomplemented
628C2×C4⋊C4D4×C4114yes—
629C2×C22⋊C4—22no—
630C2×C22⋊C4—22no—
631C2×C22⋊C4—22no—
632C2×C22⋊C4—22no—
633C2×C22⋊C4—22no—
634C2×C22⋊C4—22no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—22no—
637C2×C22⋊C4—22no—
638C2×C22⋊C4—41no—
639C2×C22⋊C4—41no—
640C2×C22⋊C4—41no—
641C2×C22⋊C4—41no—
642C2×C22⋊C4C2×C4×C4114yes—
643C2×C22⋊C4C2×C4×C4114yes—
644C2×C22⋊C4C2×C4×C4114yes—
645C2×C22⋊C4D4×C4114yes—
646C2×C22⋊C4Q8×C4114yes—
647C2×C42—22no—
648C2×C42—22no—
649C2×C42—22no—
650C2×C42—22no—
651C2×C42—41no—
652C2×C42C2×C4×C4114yescomplemented
653#95—22no—
654#95—22no—
655#95—22no—
656#95—22no—
657#95—22no—
658#95—22no—
659#95—22no—
660#95—22no—
661#95—22no—
662#95—22no—
663#95—41no—
664#95—41no—
665#95—41no—
666#95C2×C4×C4114yescomplemented
667#95C2×C4×C4114yescomplemented
668#95D4×C4114yes—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24C22×C4×C4112yes—
682C24C2×D4×C4112yes—
683C24C2×Q8×C4112yes—
684C24C24×C4111yescharacteristic
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
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—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—44no—
766C22×C4—44no—
767C22×C4—44no—
768C22×C4—44no—
769C22×C4—44no—
770C22×C4—44no—
771C22×C4—44no—
772C22×C4C22×C4×C4112yes—
773C22×C4C22×C4×C4112yes—
774C22×C4C22×C4×C4112yes—
775C22×C4C22×C4×C4112yes—
776C22×C4C22×C4×C4112yes—
777C22×C4C22×C4×C4112yes—
778C22×C4C2×D4×C4112yes—
779C22×C4C2×D4×C4112yes—
780C22×C4C2×D4×C4112yes—
781C22×C4C2×D4×C4112yes—
782C22×C4C2×D4×C4112yes—
783C22×C4C2×D4×C4112yes—
784C22×C4C2×D4×C4112yes—
785C22×C4C2×D4×C4112yes—
786C22×C4C2×Q8×C4112yes—
787C22×C4C2×Q8×C4112yes—
788C22×C4#41×C4112yes—
789C22×C4#41×C4112yes—
790C4⋊C4—28no—
791C4⋊C4—44no—
792C4⋊C4—44no—
793C4⋊C4—44no—
794C4⋊C4—44no—
795C4⋊C4—44no—
796C4⋊C4—44no—
797C4⋊C4—44no—
798C4⋊C4—44no—
799C4⋊C4—44no—
800C22⋊C4—28no—
801C22⋊C4—28no—
802C22⋊C4—44no—
803C22⋊C4—44no—
804C22⋊C4—44no—
805C22⋊C4C4⋊C4×C41116yescomplemented
806C42—28no—
807C42—44no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
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—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23C2×C4⋊C4×C4114yes—
843C23C23×C4×C4111yescharacteristic
844C23C22×D4×C4111yescharacteristic
845C23C22×D4×C4111yescharacteristic
846C23C22×D4×C4111yescharacteristic
847C23C22×Q8×C4111yescharacteristic
848C23C2×#41×C4111yescharacteristic
849C23C2×#41×C4111yescharacteristic
850C23H(5,𝔽2)×C4111yescharacteristic
851C23H(5,𝔽2)×C4111yescharacteristic
852C23H(5,𝔽2)×C4111yescharacteristic
853C23H(5,𝔽2)×C4111yescharacteristic
854C232−1+4×C4111yescharacteristic
855C232−1+4×C4111yescharacteristic
856C232−1+4×C4111yescharacteristic
857C232−1+4×C4111yescharacteristic
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—416no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4C2×C4⋊C4×C4114yes—
954C2×C4C2×C4⋊C4×C4114yes—
955C2×C4C4×D4×C4114yes—
956C2×C4C4×D4×C4114yes—
957C22—24no—
958C22—24no—
959C22—24no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—42no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22C22×C4⋊C4×C4111yescharacteristic
973C22C2×C4×D4×C4111yescharacteristic
974C22C2×C4×D4×C4111yescharacteristic
975C22C41×#52011yescharacteristic
976C22C41×#52011yescharacteristic
977C22C41×#52011yescharacteristic
978C22C41×#52011yescharacteristic
979C22C41×#53411yescharacteristic
980C22C41×#53511yescharacteristic
981C22C41×#53511yescharacteristic
982C22C41×#53611yescharacteristic
983C22C41×#53611yescharacteristic
984C22C41×#53611yescharacteristic
985C22C41×#53911yescharacteristic
986C22C41×#53911yescharacteristic
987C22C41×#54211yescharacteristic
988C22C41×#54211yescharacteristic
989C22C41×#54411yescharacteristic
990C22C41×#54411yescharacteristic
991C22D42×C4111yescharacteristic
992C22D42×C4111yescharacteristic
993C22D42×C4111yescharacteristic
994C22C41×#54711yescharacteristic
995C22C41×#54711yescharacteristic
996C22C41×#54711yescharacteristic
997C22C41×#54811yescharacteristic
998C22D4×Q8×C4111yescharacteristic
999C22D4×Q8×C4111yescharacteristic
1000C22C41×#55311yescharacteristic
1001C22C41×#55411yescharacteristic
1002C22C41×#55411yescharacteristic
1003C22C41×#56011yescharacteristic
1004C22C41×#56311yescharacteristic
1005C22C41×#56311yescharacteristic
1006C22C41×#56311yescharacteristic
1007C4—24no—
1008C4—24no—
1009C4—24no—
1010C4—24no—
1011C4—42no—
1012C4—42no—
1013C4—42no—
1014C4—42no—
1015C4—42no—
1016C4—42no—
1017C4—81no—
1018C4—81no—
1019C4—81no—
1020C4—81no—
1021C2—44no—
1022C2C41×#231711yescharacteristic
1023C2C41×#232211yescharacteristic
1024C2C41×#232611yescharacteristic
1025C2D4×C4⋊C4×C4111yescharacteristic
1026C2D4×C4⋊C4×C4111yescharacteristic
1027C2C41×#236111yescharacteristic
1028C2C41×#238311yescharacteristic
1029C2C41×#266911yescharacteristic
1030C2C41×#267411yescharacteristic
1031C2C41×#267711yescharacteristic
1032C2C41×#268011yescharacteristic
1033C2C41×#271811yescharacteristic
1034C2C41×#272011yescharacteristic
1035C2C41×#272911yescharacteristic
1036C2C41×#279011yescharacteristic
subgroupG/H
center, socleC24×C41C24
commutatorC23C23×C4×C41
Frattini, cosocleC24C24×C41
prime radicalC25×C41C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C41×#389C2semidirect
7. C2×C41×#384C2semidirect
8. C41×#1444C2semidirect
9. C41×#1444C2semidirect
10. C41×#1442C2semidirect
11. C41×#1441C2semidirect
14. C41×#1436C2semidirect
15. C41×#1434C2semidirect
37. C41×#388C4semidirect
108. C2×C4⋊C4×C41C2×C4semidirect
133. C2×C42×C41C2×C4semidirect
147. #95×C41C2×C4semidirect
148. #95×C41C2×C4semidirect
286. C22⋊C4×C41C4⋊C4semidirect
438. #14405C41direct (N × H)
503. C2×#389C2×C41semidirect
509. C2×#384C2×C41semidirect
510. #1444C2×C41semidirect
511. #1444C2×C41semidirect
512. #1442C2×C41semidirect
513. #1441C2×C41semidirect
516. #1436C2×C41semidirect
517. #1434C2×C41semidirect
555. #388C4×C41semidirect
576. C41#14405direct (N × H)
627. C2×C4⋊C4C2×C4×C41semidirect
652. C2×C42C2×C4×C41semidirect
666. #95C2×C4×C41semidirect
667. #95C2×C4×C41semidirect
805. C22⋊C4C4⋊C4×C41semidirect

Maximal subgroups

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

subgroupindex
C2×C41×#3892
C2×C41×#3882
C2×C41×#3852
C2×C41×#3842
C41×#14442
C41×#14422
C41×#14412
C41×#14392
C41×#14362
C41×#14342
#1440541