Finite Group Databasebeta

← C41×#14403 #23790604

Subgroups — C41×#14403 #23790604

Order 10496.

1650 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#388C211yesmaximal, characteristic
2C2×C41×#388C211yesmaximal, characteristic
3C2×C41×#385C211yesmaximal, characteristic
4C2×C41×#385C211yesmaximal, characteristic
5C2×C41×#382C211yesmaximal, characteristic, complemented
6C41×#1444C211yesmaximal, characteristic, complemented
7C41×#1444C211yesmaximal, characteristic, complemented
8C41×#1442C211yesmaximal, characteristic, complemented
9C41×#1441C211yesmaximal, characteristic, complemented
10C41×#1439C211yesmaximal, characteristic
11C41×#1439C211yesmaximal, characteristic
12C41×#1436C211yesmaximal, characteristic, complemented
13C41×C4⋊#95C211yesmaximal, characteristic, complemented
14C41×C4⋊#95C211yesmaximal, characteristic, complemented
15C41×C22⋊#95C211yesmaximal, characteristic
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×C22⋊C4×C41C2211yescharacteristic
26C22×C22⋊C4×C41C2211yescharacteristic
27C22×C22⋊C4×C41C2211yescharacteristic
28C22×C22⋊C4×C41C2211yescharacteristic
29C22×C22⋊C4×C41C2211yescharacteristic
30C22×C22⋊C4×C41C2211yescharacteristic
31C22×C42×C41C2211yescharacteristic
32C22×C42×C41C2211yescharacteristic
33C41×#388—24no—
34C41×#388C418yescomplemented
35C41×#385—24no—
36C41×#385—24no—
37C41×#382—24no—
38C2×#95×C41C2211yescharacteristic
39C2×#95×C41C2211yescharacteristic
40C2×#95×C41C2211yescharacteristic
41C2×#95×C41C2211yescharacteristic
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
56C25×C41C2311yescharacteristic
57C23×C4×C41—22no—
58C23×C4×C41—22no—
59C23×C4×C41—22no—
60C23×C4×C41—41no—
61C23×C4×C41—41no—
62C23×C4×C41—41no—
63C23×C4×C41—41no—
64C23×C4×C41C2311yescharacteristic
65C23×C4×C41C2311yescharacteristic
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
78C2×C4⋊C4×C41—22no—
79C2×C4⋊C4×C41—22no—
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—41no—
90C2×C4⋊C4×C41—41no—
91C2×C4⋊C4×C41—41no—
92C2×C4⋊C4×C41—41no—
93C2×C4⋊C4×C41—41no—
94C2×C4⋊C4×C41—41no—
95C2×C4⋊C4×C41—41no—
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×C41C2×C414yescomplemented
102C2×C22⋊C4×C41—22no—
103C2×C22⋊C4×C41—22no—
104C2×C22⋊C4×C41—22no—
105C2×C22⋊C4×C41—22no—
106C2×C22⋊C4×C41—22no—
107C2×C22⋊C4×C41—22no—
108C2×C22⋊C4×C41—22no—
109C2×C22⋊C4×C41—41no—
110C2×C22⋊C4×C41—41no—
111C2×C22⋊C4×C41—41no—
112C2×C22⋊C4×C41—41no—
113C2×C22⋊C4×C41—41no—
114C2×C22⋊C4×C41—41no—
115C2×C22⋊C4×C41C2×C414yes—
116C2×C22⋊C4×C41C2×C414yes—
117C2×C22⋊C4×C41C2×C414yes—
118C2×C22⋊C4×C41D414yes—
119C2×C22⋊C4×C41Q814yes—
120C2×C42×C41—22no—
121C2×C42×C41—22no—
122C2×C42×C41—22no—
123C2×C42×C41—22no—
124C2×C42×C41—41no—
125C2×C42×C41C2×C414yescomplemented
126#95×C41—22no—
127#95×C41—22no—
128#95×C41—22no—
129#95×C41—22no—
130#95×C41—22no—
131#95×C41—22no—
132#95×C41—22no—
133#95×C41—22no—
134#95×C41—41no—
135#95×C41—41no—
136#95×C41—41no—
137#95×C41—41no—
138#95×C41—41no—
139#95×C41—41no—
140#95×C41—41no—
141#95×C41C2×C414yescomplemented
142#95×C41C2×C414yescomplemented
143#95×C41D414yes—
144C24×C41—21no—
145C24×C41—21no—
146C24×C41—21no—
147C24×C41—21no—
148C24×C41—21no—
149C24×C41—21no—
150C24×C41—21no—
151C24×C41—21no—
152C24×C41—21no—
153C24×C41—21no—
154C24×C41—21no—
155C24×C41—21no—
156C24×C41C22×C412yes—
157C24×C41C2×D412yes—
158C24×C41C2×Q812yes—
159C24×C41C2411yescharacteristic
160C22×C4×C41—21no—
161C22×C4×C41—21no—
162C22×C4×C41—21no—
163C22×C4×C41—21no—
164C22×C4×C41—21no—
165C22×C4×C41—21no—
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—44no—
243C22×C4×C41—44no—
244C22×C4×C41—44no—
245C22×C4×C41—44no—
246C22×C4×C41—44no—
247C22×C4×C41—44no—
248C22×C4×C41—44no—
249C22×C4×C41C22×C412yes—
250C22×C4×C41C22×C412yes—
251C22×C4×C41C22×C412yes—
252C22×C4×C41C22×C412yes—
253C22×C4×C41C22×C412yes—
254C22×C4×C41C22×C412yes—
255C22×C4×C41C2×D412yes—
256C22×C4×C41C2×D412yes—
257C22×C4×C41C2×D412yes—
258C22×C4×C41C2×D412yes—
259C22×C4×C41C2×D412yes—
260C22×C4×C41C2×Q812yes—
261C22×C4×C41C2×Q812yes—
262C22×C4×C41#4112yes—
263C22×C4×C41#4112yes—
264C22×C4×C41#4112yes—
265C4⋊C4×C41—44no—
266C4⋊C4×C41—44no—
267C4⋊C4×C41—44no—
268C4⋊C4×C41—44no—
269C4⋊C4×C41—44no—
270C4⋊C4×C41—44no—
271C4⋊C4×C41—44no—
272C4⋊C4×C41—44no—
273C22⋊C4×C41—28no—
274C22⋊C4×C41—44no—
275C22⋊C4×C41—44no—
276C22⋊C4×C41—44no—
277C22⋊C4×C41—44no—
278C22⋊C4×C41C4⋊C4116yescomplemented
279C42×C41—28no—
280C42×C41—44no—
281C23×C41—22no—
282C23×C41—22no—
283C23×C41—22no—
284C23×C41—22no—
285C23×C41—22no—
286C23×C41—22no—
287C23×C41—22no—
288C23×C41—22no—
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—41no—
300C23×C41—41no—
301C23×C41—41no—
302C23×C41—41no—
303C23×C41—41no—
304C23×C41—41no—
305C23×C41—41no—
306C23×C41—41no—
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×C41C2×C4⋊C414yes—
316C23×C41C23×C411yescharacteristic
317C23×C41C22×D411yescharacteristic
318C23×C41C22×D411yescharacteristic
319C23×C41C22×Q811yescharacteristic
320C23×C41C2×#4111yescharacteristic
321C23×C41C2×#4111yescharacteristic
322C23×C41C2×#4111yescharacteristic
323C23×C41H(5,𝔽2)11yescharacteristic
324C23×C41H(5,𝔽2)11yescharacteristic
325C23×C41H(5,𝔽2)11yescharacteristic
326C23×C41H(5,𝔽2)11yescharacteristic
327C23×C41H(5,𝔽2)11yescharacteristic
328C23×C412−1+411yescharacteristic
329C23×C412−1+411yescharacteristic
330C23×C412−1+411yescharacteristic
331C2×C4×C41—22no—
332C2×C4×C41—22no—
333C2×C4×C41—22no—
334C2×C4×C41—22no—
335C2×C4×C41—22no—
336C2×C4×C41—22no—
337C2×C4×C41—22no—
338C2×C4×C41—22no—
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—416no—
371C2×C4×C41—41no—
372C2×C4×C41—41no—
373C2×C4×C41—41no—
374C2×C4×C41—41no—
375C2×C4×C41—41no—
376C2×C4×C41—41no—
377C2×C4×C41—41no—
378C2×C4×C41—41no—
379C2×C4×C41—41no—
380C2×C4×C41—41no—
381C2×C4×C41—41no—
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×C41C2×C4⋊C414yes—
428C2×C4×C41C2×C4⋊C414yes—
429C2×C4×C41C4×D414yes—
430#14403C4111yesmaximal, characteristic, direct product factor, Sylow
431C22×C41—24no—
432C22×C41—24no—
433C22×C41—24no—
434C22×C41—42no—
435C22×C41—42no—
436C22×C41—42no—
437C22×C41—42no—
438C22×C41—42no—
439C22×C41—42no—
440C22×C41—42no—
441C22×C41—42no—
442C22×C41—42no—
443C22×C41—42no—
444C22×C41—42no—
445C22×C41—42no—
446C22×C41C22×C4⋊C411yescharacteristic
447C22×C41C2×C4×D411yescharacteristic
448C22×C41C4×#4111yescharacteristic
449C22×C41#51811yescharacteristic
450C22×C41#52011yescharacteristic
451C22×C41#52011yescharacteristic
452C22×C41#52011yescharacteristic
453C22×C41#53511yescharacteristic
454C22×C41#53511yescharacteristic
455C22×C41#53611yescharacteristic
456C22×C41#53711yescharacteristic
457C22×C41#53811yescharacteristic
458C22×C41#53911yescharacteristic
459C22×C41#54011yescharacteristic
460C22×C41#54111yescharacteristic
461C22×C41#54211yescharacteristic
462C22×C41#54211yescharacteristic
463C22×C41#54411yescharacteristic
464C22×C41#54411yescharacteristic
465C22×C41D4211yescharacteristic
466C22×C41#54611yescharacteristic
467C22×C41#54611yescharacteristic
468C22×C41#54611yescharacteristic
469C22×C41#54711yescharacteristic
470C22×C41#54711yescharacteristic
471C22×C41D4×Q811yescharacteristic
472C22×C41#55111yescharacteristic
473C22×C41#55211yescharacteristic
474C22×C41#55411yescharacteristic
475C22×C41#55411yescharacteristic
476C22×C41#55411yescharacteristic
477C22×C41H(3,𝔽4)11yescharacteristic
478C22×C41#56211yescharacteristic
479C22×C41#56211yescharacteristic
480C22×C41#56311yescharacteristic
481C4×C41—24no—
482C4×C41—24no—
483C4×C41—24no—
484C4×C41—42no—
485C4×C41—42no—
486C4×C41—42no—
487C4×C41—42no—
488C4×C41—42no—
489C4×C41—42no—
490C4×C41—42no—
491C4×C41—81no—
492C4×C41—81no—
493C4×C41—81no—
494C4×C41—81no—
495C2×#388C2×C4111yescharacteristic
496C2×#388C2×C4111yescharacteristic
497C2×#385C2×C4111yescharacteristic
498C2×#385C2×C4111yescharacteristic
499C2×#382C2×C4111yescharacteristic, complemented
500#1444C2×C4111yescharacteristic, complemented
501#1444C2×C4111yescharacteristic, complemented
502#1442C2×C4111yescharacteristic, complemented
503#1441C2×C4111yescharacteristic, complemented
504#1439C2×C4111yescharacteristic
505#1439C2×C4111yescharacteristic
506#1436C2×C4111yescharacteristic, complemented
507C4⋊#95C2×C4111yescharacteristic, complemented
508C4⋊#95C2×C4111yescharacteristic, complemented
509C22⋊#95C2×C4111yescharacteristic
510C2×C41—44no—
511C2×C41#231711yescharacteristic
512C2×C41#232411yescharacteristic
513C2×C41#233411yescharacteristic
514C2×C41D4×C4⋊C411yescharacteristic
515C2×C41#234911yescharacteristic
516C2×C41#235911yescharacteristic
517C2×C41#237911yescharacteristic
518C2×C41#267011yescharacteristic
519C2×C41#267211yescharacteristic
520C2×C41#269811yescharacteristic
521C2×C41#270411yescharacteristic
522C2×C41#270611yescharacteristic
523C2×C41#272011yescharacteristic
524C2×C41#276311yescharacteristic
525C2×C41#276811yescharacteristic
526C24×C4C22×C4111yescharacteristic
527C22×C4⋊C4C22×C4111yescharacteristic
528C22×C4⋊C4C22×C4111yescharacteristic
529C22×C4⋊C4C22×C4111yescharacteristic
530C22×C4⋊C4C22×C4111yescharacteristic
531C22×C4⋊C4C22×C4111yescharacteristic
532C22×C4⋊C4C22×C4111yescharacteristic
533C22×C4⋊C4C22×C4111yescharacteristic
534C22×C4⋊C4C22×C4111yescharacteristic
535C22×C22⋊C4C22×C4111yescharacteristic
536C22×C22⋊C4C22×C4111yescharacteristic
537C22×C22⋊C4C22×C4111yescharacteristic
538C22×C22⋊C4C22×C4111yescharacteristic
539C22×C22⋊C4C22×C4111yescharacteristic
540C22×C22⋊C4C22×C4111yescharacteristic
541C22×C42C22×C4111yescharacteristic
542C22×C42C22×C4111yescharacteristic
543#388—24no—
544#388C4×C4118yescomplemented
545#385—24no—
546#385—24no—
547#382—24no—
548C2×#95C22×C4111yescharacteristic
549C2×#95C22×C4111yescharacteristic
550C2×#95C22×C4111yescharacteristic
551C2×#95C22×C4111yescharacteristic
552C2×#95C22×C4111yescharacteristic
553C2×#95C22×C4111yescharacteristic
554C2×#95C22×C4111yescharacteristic
555C2×#95C22×C4111yescharacteristic
556C2×#95C22×C4111yescharacteristic
557C2×#95C22×C4111yescharacteristic
558C2×#95C22×C4111yescharacteristic
559C2×#95C22×C4111yescharacteristic
560C2×#95C22×C4111yescharacteristic
561C2×#95C22×C4111yescharacteristic
562C2×#95C22×C4111yescharacteristic
563C2×#95C22×C4111yescharacteristic
564C2×#95C22×C4111yescharacteristic
565C2×#95C22×C4111yescharacteristic
566C41#1440311yescharacteristic, direct product factor, Sylow
567C25C23×C4111yescharacteristic
568C23×C4—22no—
569C23×C4—22no—
570C23×C4—22no—
571C23×C4—41no—
572C23×C4—41no—
573C23×C4—41no—
574C23×C4—41no—
575C23×C4C23×C4111yescharacteristic
576C23×C4C23×C4111yescharacteristic
577C23×C4C23×C4111yescharacteristic
578C23×C4C23×C4111yescharacteristic
579C23×C4C23×C4111yescharacteristic
580C23×C4C23×C4111yescharacteristic
581C23×C4C23×C4111yescharacteristic
582C23×C4C23×C4111yescharacteristic
583C23×C4C23×C4111yescharacteristic
584C23×C4C23×C4111yescharacteristic
585C23×C4C23×C4111yescharacteristic
586C23×C4C23×C4111yescharacteristic
587C23×C4C23×C4111yescharacteristic
588C23×C4C23×C4111yescharacteristic
589C2×C4⋊C4—22no—
590C2×C4⋊C4—22no—
591C2×C4⋊C4—22no—
592C2×C4⋊C4—22no—
593C2×C4⋊C4—22no—
594C2×C4⋊C4—22no—
595C2×C4⋊C4—22no—
596C2×C4⋊C4—22no—
597C2×C4⋊C4—22no—
598C2×C4⋊C4—22no—
599C2×C4⋊C4—22no—
600C2×C4⋊C4—41no—
601C2×C4⋊C4—41no—
602C2×C4⋊C4—41no—
603C2×C4⋊C4—41no—
604C2×C4⋊C4—41no—
605C2×C4⋊C4—41no—
606C2×C4⋊C4—41no—
607C2×C4⋊C4—41no—
608C2×C4⋊C4—41no—
609C2×C4⋊C4—41no—
610C2×C4⋊C4—41no—
611C2×C4⋊C4—41no—
612C2×C4⋊C4C2×C4×C4114yescomplemented
613C2×C22⋊C4—22no—
614C2×C22⋊C4—22no—
615C2×C22⋊C4—22no—
616C2×C22⋊C4—22no—
617C2×C22⋊C4—22no—
618C2×C22⋊C4—22no—
619C2×C22⋊C4—22no—
620C2×C22⋊C4—41no—
621C2×C22⋊C4—41no—
622C2×C22⋊C4—41no—
623C2×C22⋊C4—41no—
624C2×C22⋊C4—41no—
625C2×C22⋊C4—41no—
626C2×C22⋊C4C2×C4×C4114yes—
627C2×C22⋊C4C2×C4×C4114yes—
628C2×C22⋊C4C2×C4×C4114yes—
629C2×C22⋊C4D4×C4114yes—
630C2×C22⋊C4Q8×C4114yes—
631C2×C42—22no—
632C2×C42—22no—
633C2×C42—22no—
634C2×C42—22no—
635C2×C42—41no—
636C2×C42C2×C4×C4114yescomplemented
637#95—22no—
638#95—22no—
639#95—22no—
640#95—22no—
641#95—22no—
642#95—22no—
643#95—22no—
644#95—22no—
645#95—41no—
646#95—41no—
647#95—41no—
648#95—41no—
649#95—41no—
650#95—41no—
651#95—41no—
652#95C2×C4×C4114yescomplemented
653#95C2×C4×C4114yescomplemented
654#95D4×C4114yes—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24C22×C4×C4112yes—
668C24C2×D4×C4112yes—
669C24C2×Q8×C4112yes—
670C24C24×C4111yescharacteristic
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
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—44no—
754C22×C4—44no—
755C22×C4—44no—
756C22×C4—44no—
757C22×C4—44no—
758C22×C4—44no—
759C22×C4—44no—
760C22×C4C22×C4×C4112yes—
761C22×C4C22×C4×C4112yes—
762C22×C4C22×C4×C4112yes—
763C22×C4C22×C4×C4112yes—
764C22×C4C22×C4×C4112yes—
765C22×C4C22×C4×C4112yes—
766C22×C4C2×D4×C4112yes—
767C22×C4C2×D4×C4112yes—
768C22×C4C2×D4×C4112yes—
769C22×C4C2×D4×C4112yes—
770C22×C4C2×D4×C4112yes—
771C22×C4C2×Q8×C4112yes—
772C22×C4C2×Q8×C4112yes—
773C22×C4#41×C4112yes—
774C22×C4#41×C4112yes—
775C22×C4#41×C4112yes—
776C4⋊C4—44no—
777C4⋊C4—44no—
778C4⋊C4—44no—
779C4⋊C4—44no—
780C4⋊C4—44no—
781C4⋊C4—44no—
782C4⋊C4—44no—
783C4⋊C4—44no—
784C22⋊C4—28no—
785C22⋊C4—44no—
786C22⋊C4—44no—
787C22⋊C4—44no—
788C22⋊C4—44no—
789C22⋊C4C4⋊C4×C41116yescomplemented
790C42—28no—
791C42—44no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23C2×C4⋊C4×C4114yes—
827C23C23×C4×C4111yescharacteristic
828C23C22×D4×C4111yescharacteristic
829C23C22×D4×C4111yescharacteristic
830C23C22×Q8×C4111yescharacteristic
831C23C2×#41×C4111yescharacteristic
832C23C2×#41×C4111yescharacteristic
833C23C2×#41×C4111yescharacteristic
834C23H(5,𝔽2)×C4111yescharacteristic
835C23H(5,𝔽2)×C4111yescharacteristic
836C23H(5,𝔽2)×C4111yescharacteristic
837C23H(5,𝔽2)×C4111yescharacteristic
838C23H(5,𝔽2)×C4111yescharacteristic
839C232−1+4×C4111yescharacteristic
840C232−1+4×C4111yescharacteristic
841C232−1+4×C4111yescharacteristic
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
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—416no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
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×C4C2×C4⋊C4×C4114yes—
939C2×C4C2×C4⋊C4×C4114yes—
940C2×C4C4×D4×C4114yes—
941C22—24no—
942C22—24no—
943C22—24no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22C22×C4⋊C4×C4111yescharacteristic
957C22C2×C4×D4×C4111yescharacteristic
958C22C4×#41×C4111yescharacteristic
959C22C41×#51811yescharacteristic
960C22C41×#52011yescharacteristic
961C22C41×#52011yescharacteristic
962C22C41×#52011yescharacteristic
963C22C41×#53511yescharacteristic
964C22C41×#53511yescharacteristic
965C22C41×#53611yescharacteristic
966C22C41×#53711yescharacteristic
967C22C41×#53811yescharacteristic
968C22C41×#53911yescharacteristic
969C22C41×#54011yescharacteristic
970C22C41×#54111yescharacteristic
971C22C41×#54211yescharacteristic
972C22C41×#54211yescharacteristic
973C22C41×#54411yescharacteristic
974C22C41×#54411yescharacteristic
975C22D42×C4111yescharacteristic
976C22C41×#54611yescharacteristic
977C22C41×#54611yescharacteristic
978C22C41×#54611yescharacteristic
979C22C41×#54711yescharacteristic
980C22C41×#54711yescharacteristic
981C22D4×Q8×C4111yescharacteristic
982C22C41×#55111yescharacteristic
983C22C41×#55211yescharacteristic
984C22C41×#55411yescharacteristic
985C22C41×#55411yescharacteristic
986C22C41×#55411yescharacteristic
987C22C41×H(3,𝔽4)11yescharacteristic
988C22C41×#56211yescharacteristic
989C22C41×#56211yescharacteristic
990C22C41×#56311yescharacteristic
991C4—24no—
992C4—24no—
993C4—24no—
994C4—42no—
995C4—42no—
996C4—42no—
997C4—42no—
998C4—42no—
999C4—42no—
1000C4—42no—
1001C4—81no—
1002C4—81no—
1003C4—81no—
1004C4—81no—
1005C2—44no—
1006C2C41×#231711yescharacteristic
1007C2C41×#232411yescharacteristic
1008C2C41×#233411yescharacteristic
1009C2D4×C4⋊C4×C4111yescharacteristic
1010C2C41×#234911yescharacteristic
1011C2C41×#235911yescharacteristic
1012C2C41×#237911yescharacteristic
1013C2C41×#267011yescharacteristic
1014C2C41×#267211yescharacteristic
1015C2C41×#269811yescharacteristic
1016C2C41×#270411yescharacteristic
1017C2C41×#270611yescharacteristic
1018C2C41×#272011yescharacteristic
1019C2C41×#276311yescharacteristic
1020C2C41×#276811yescharacteristic
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
5. C2×C41×#382C2semidirect
6. C41×#1444C2semidirect
7. C41×#1444C2semidirect
8. C41×#1442C2semidirect
9. C41×#1441C2semidirect
12. C41×#1436C2semidirect
13. C41×C4⋊#95C2semidirect
14. C41×C4⋊#95C2semidirect
34. C41×#388C4semidirect
101. C2×C4⋊C4×C41C2×C4semidirect
125. C2×C42×C41C2×C4semidirect
141. #95×C41C2×C4semidirect
142. #95×C41C2×C4semidirect
278. C22⋊C4×C41C4⋊C4semidirect
430. #14403C41direct (N × H)
499. C2×#382C2×C41semidirect
500. #1444C2×C41semidirect
501. #1444C2×C41semidirect
502. #1442C2×C41semidirect
503. #1441C2×C41semidirect
506. #1436C2×C41semidirect
507. C4⋊#95C2×C41semidirect
508. C4⋊#95C2×C41semidirect
544. #388C4×C41semidirect
566. C41#14403direct (N × H)
612. C2×C4⋊C4C2×C4×C41semidirect
636. C2×C42C2×C4×C41semidirect
652. #95C2×C4×C41semidirect
653. #95C2×C4×C41semidirect
789. 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×#3882
C2×C41×#3852
C2×C41×#3822
C41×#14442
C41×#14422
C41×#14412
C41×#14392
C41×#14362
C41×C4⋊#952
C41×C22⋊#952
#1440341