Finite Group Databasebeta

← C41×#14200 #23790401

Subgroups — C41×#14200 #23790401

Order 10496.

1686 conjugacy classes of subgroups.

The subgroup lattice has 1016 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#396C211yesmaximal, characteristic
2C2×C41×#389C211yesmaximal, characteristic, complemented
3C2×C41×#388C211yesmaximal, characteristic
4C2×C41×#388C211yesmaximal, characteristic
5C2×C41×#388C211yesmaximal, characteristic
6C2×C4×C4⋊C4×C41C211yesmaximal, characteristic, complemented
7C2×C4×C4⋊C4×C41C211yesmaximal, characteristic, complemented
8C41×#1441C211yesmaximal, characteristic, complemented
9C41×#1441C211yesmaximal, characteristic, complemented
10C41×#1439C211yesmaximal, characteristic
11C41×#1437C211yesmaximal, characteristic
12C41×#1437C211yesmaximal, characteristic
13C41×#1436C211yesmaximal, characteristic, complemented
14C41×#1436C211yesmaximal, characteristic, complemented
15C41×#1434C211yesmaximal, characteristic, complemented
16C22×C4⋊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×C22⋊C4×C41C2211yescharacteristic
24C22×C22⋊C4×C41C2211yescharacteristic
25C22×C22⋊C4×C41C2211yescharacteristic
26C22×C22⋊C4×C41C2211yescharacteristic
27C22×C22⋊C4×C41C2211yescharacteristic
28C22×C22⋊C4×C41C2211yescharacteristic
29C22×C22⋊C4×C41C2211yescharacteristic
30C22×C42×C41C2211yescharacteristic
31C22×C42×C41C2211yescharacteristic
32C22×C42×C41C2211yescharacteristic
33C22×C42×C41C2211yescharacteristic
34C22×C42×C41C2211yescharacteristic
35C41×#396C418yescomplemented
36C41×#389—24no—
37C41×#388—24no—
38C41×#388—24no—
39C41×#388—24no—
40C4×C4⋊C4×C41—24no—
41C4×C4⋊C4×C41—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×C41C2311yescharacteristic
60C23×C4×C41C2311yescharacteristic
61C23×C4×C41C2311yescharacteristic
62C23×C4×C41C2311yescharacteristic
63C23×C4×C41C2311yescharacteristic
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
73C2×C4⋊C4×C41—22no—
74C2×C4⋊C4×C41—22no—
75C2×C4⋊C4×C41—22no—
76C2×C4⋊C4×C41—22no—
77C2×C4⋊C4×C41—22no—
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×C41C2×C414yes—
91C2×C4⋊C4×C41C2×C414yes—
92C2×C4⋊C4×C41C2×C414yes—
93C2×C4⋊C4×C41D414yes—
94C2×C22⋊C4×C41—22no—
95C2×C22⋊C4×C41—22no—
96C2×C22⋊C4×C41—22no—
97C2×C22⋊C4×C41—22no—
98C2×C22⋊C4×C41—22no—
99C2×C22⋊C4×C41—22no—
100C2×C22⋊C4×C41—22no—
101C2×C22⋊C4×C41—22no—
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—22no—
110C2×C22⋊C4×C41—41no—
111C2×C22⋊C4×C41—41no—
112C2×C22⋊C4×C41C2×C414yes—
113C2×C22⋊C4×C41C2×C414yes—
114C2×C22⋊C4×C41C2×C414yes—
115C2×C42×C41—22no—
116C2×C42×C41—22no—
117C2×C42×C41—22no—
118C2×C42×C41—22no—
119C2×C42×C41—22no—
120C2×C42×C41—22no—
121C2×C42×C41—22no—
122C2×C42×C41—22no—
123C2×C42×C41—22no—
124C2×C42×C41—22no—
125C2×C42×C41—22no—
126C2×C42×C41—22no—
127C2×C42×C41—41no—
128C2×C42×C41—41no—
129C2×C42×C41D414yes—
130#95×C41—22no—
131#95×C41—22no—
132#95×C41—22no—
133#95×C41—22no—
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—41no—
144#95×C41C2×C414yes—
145#95×C41D414yes—
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×C41—21no—
157C24×C41—21no—
158C24×C41—21no—
159C24×C41—21no—
160C24×C41C22×C412yes—
161C24×C41C2411yescharacteristic
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×C41C22×C412yes—
239C22×C4×C41C22×C412yes—
240C22×C4×C41C22×C412yes—
241C22×C4×C41C22×C412yes—
242C22×C4×C41C22×C412yes—
243C22×C4×C41C22×C412yes—
244C22×C4×C41C2×D412yes—
245C22×C4×C41C2×D412yes—
246C22×C4×C41C2×D412yes—
247C22×C4×C41C2×D412yes—
248C22×C4×C41C2×D412yes—
249C22×C4×C41C2×D412yes—
250C22×C4×C41C2×D412yes—
251C22×C4×C41C2×D412yes—
252C22×C4×C41C2×D412yes—
253C22×C4×C41#4112yes—
254C22×C4×C41#4112yes—
255C22×C4×C41#4112yes—
256C22×C4×C41#4112yes—
257C22×C4×C41#4112yes—
258C22×C4×C41#4112yes—
259C22×C4×C41#4112yes—
260C4⋊C4×C41—28no—
261C4⋊C4×C41—28no—
262C4⋊C4×C41—28no—
263C4⋊C4×C41—28no—
264C4⋊C4×C41—28no—
265C4⋊C4×C41—44no—
266C4⋊C4×C41—44no—
267C22⋊C4×C41—28no—
268C22⋊C4×C41—28no—
269C22⋊C4×C41—28no—
270C22⋊C4×C41—44no—
271C22⋊C4×C41—44no—
272C22⋊C4×C41—44no—
273C22⋊C4×C41—44no—
274C42×C41—28no—
275C42×C41—28no—
276C42×C41—44no—
277C42×C41—44no—
278C42×C41—44no—
279C23×C41—22no—
280C23×C41—22no—
281C23×C41—22no—
282C23×C41—22no—
283C23×C41—22no—
284C23×C41—22no—
285C23×C41—22no—
286C23×C41—41no—
287C23×C41—41no—
288C23×C41—41no—
289C23×C41—41no—
290C23×C41—41no—
291C23×C41—41no—
292C23×C41—41no—
293C23×C41—41no—
294C23×C41—41no—
295C23×C41—41no—
296C23×C41—41no—
297C23×C41—41no—
298C23×C41—41no—
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×C41C23×C411yescharacteristic
315C23×C41C22×D411yescharacteristic
316C23×C41C22×D411yescharacteristic
317C23×C41C22×D411yescharacteristic
318C23×C41C2×#4111yescharacteristic
319C23×C41C2×#4111yescharacteristic
320C23×C41C2×#4111yescharacteristic
321C23×C41C2×#4111yescharacteristic
322C23×C41C2×#4111yescharacteristic
323C23×C41C2×#4111yescharacteristic
324C23×C41C2×#4111yescharacteristic
325C23×C41H(5,𝔽2)11yescharacteristic
326C23×C412−1+411yescharacteristic
327C23×C412−1+411yescharacteristic
328C23×C412−1+411yescharacteristic
329C2×C4×C41—22no—
330C2×C4×C41—22no—
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—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—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×C41C4×D414yes—
423C2×C4×C41C4×D414yes—
424C2×C4×C41C4×D414yes—
425C2×C4×C41#12114yes—
426C2×C4×C41#12114yes—
427#14200C4111yesmaximal, characteristic, direct product factor, Sylow
428C22×C41—42no—
429C22×C41—42no—
430C22×C41—42no—
431C22×C41—42no—
432C22×C41—42no—
433C22×C41—42no—
434C22×C41—42no—
435C22×C41—81no—
436C22×C41—81no—
437C22×C41—81no—
438C22×C41—81no—
439C22×C41—81no—
440C22×C41—81no—
441C22×C41—81no—
442C22×C41—81no—
443C22×C41C2×C4×D411yescharacteristic
444C22×C41C2×C4×D411yescharacteristic
445C22×C41C2×C4×D411yescharacteristic
446C22×C41C4×#4111yescharacteristic
447C22×C41C4×#4111yescharacteristic
448C22×C41#51911yescharacteristic
449C22×C41#52011yescharacteristic
450C22×C41C2×#12111yescharacteristic
451C22×C41C2×#12111yescharacteristic
452C22×C41#52511yescharacteristic
453C22×C41#52511yescharacteristic
454C22×C41#52911yescharacteristic
455C22×C41#52911yescharacteristic
456C22×C41#53211yescharacteristic
457C22×C41#53211yescharacteristic
458C22×C41#53611yescharacteristic
459C22×C41#53711yescharacteristic
460C22×C41#54111yescharacteristic
461C22×C41#54211yescharacteristic
462C22×C41D4211yescharacteristic
463C22×C41#54711yescharacteristic
464C22×C41#54711yescharacteristic
465C22×C41#54711yescharacteristic
466C22×C41#54811yescharacteristic
467C22×C41#54811yescharacteristic
468C22×C41#54811yescharacteristic
469C22×C41#55111yescharacteristic
470C22×C41#55211yescharacteristic
471C22×C41#55211yescharacteristic
472C22×C41#55211yescharacteristic
473C22×C41#55311yescharacteristic
474C22×C41#55311yescharacteristic
475C22×C41#55611yescharacteristic
476C22×C41#55611yescharacteristic
477C22×C41#55611yescharacteristic
478C4×C41—24no—
479C4×C41—24no—
480C4×C41—24no—
481C4×C41—24no—
482C4×C41—24no—
483C4×C41—42no—
484C4×C41—42no—
485C4×C41—42no—
486C4×C41—42no—
487C4×C41—42no—
488C4×C41—42no—
489C4×C41—42no—
490C4×C41—81no—
491C4×C41—81no—
492C2×#396C2×C4111yescharacteristic
493C2×#389C2×C4111yescharacteristic, complemented
494C2×#388C2×C4111yescharacteristic
495C2×#388C2×C4111yescharacteristic
496C2×#388C2×C4111yescharacteristic
497C2×C4×C4⋊C4C2×C4111yescharacteristic, complemented
498C2×C4×C4⋊C4C2×C4111yescharacteristic, complemented
499#1441C2×C4111yescharacteristic, complemented
500#1441C2×C4111yescharacteristic, complemented
501#1439C2×C4111yescharacteristic
502#1437C2×C4111yescharacteristic
503#1437C2×C4111yescharacteristic
504#1436C2×C4111yescharacteristic, complemented
505#1436C2×C4111yescharacteristic, complemented
506#1434C2×C4111yescharacteristic, complemented
507C2×C41—82no—
508C2×C41C4×#12111yescharacteristic
509C2×C41C4×#12111yescharacteristic
510C2×C41#232311yescharacteristic
511C2×C41#236111yescharacteristic
512C2×C41#236211yescharacteristic
513C2×C41#236211yescharacteristic
514C2×C41#237311yescharacteristic
515C2×C41#241311yescharacteristic
516C2×C41#241611yescharacteristic
517C2×C41#246111yescharacteristic
518C2×C41#246911yescharacteristic
519C2×C41#251911yescharacteristic
520C2×C41#252511yescharacteristic
521C2×C41#254511yescharacteristic
522C2×C41#260111yescharacteristic
523C22×C4⋊C4C22×C4111yescharacteristic
524C22×C4⋊C4C22×C4111yescharacteristic
525C22×C4⋊C4C22×C4111yescharacteristic
526C22×C4⋊C4C22×C4111yescharacteristic
527C22×C4⋊C4C22×C4111yescharacteristic
528C22×C4⋊C4C22×C4111yescharacteristic
529C22×C4⋊C4C22×C4111yescharacteristic
530C22×C22⋊C4C22×C4111yescharacteristic
531C22×C22⋊C4C22×C4111yescharacteristic
532C22×C22⋊C4C22×C4111yescharacteristic
533C22×C22⋊C4C22×C4111yescharacteristic
534C22×C22⋊C4C22×C4111yescharacteristic
535C22×C22⋊C4C22×C4111yescharacteristic
536C22×C22⋊C4C22×C4111yescharacteristic
537C22×C42C22×C4111yescharacteristic
538C22×C42C22×C4111yescharacteristic
539C22×C42C22×C4111yescharacteristic
540C22×C42C22×C4111yescharacteristic
541C22×C42C22×C4111yescharacteristic
542#396C4×C4118yescomplemented
543#389—24no—
544#388—24no—
545#388—24no—
546#388—24no—
547C4×C4⋊C4—24no—
548C4×C4⋊C4—24no—
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
565C41#1420011yescharacteristic, direct product factor, Sylow
566C25C23×C4111yescharacteristic
567C23×C4C23×C4111yescharacteristic
568C23×C4C23×C4111yescharacteristic
569C23×C4C23×C4111yescharacteristic
570C23×C4C23×C4111yescharacteristic
571C23×C4C23×C4111yescharacteristic
572C23×C4C23×C4111yescharacteristic
573C23×C4C23×C4111yescharacteristic
574C23×C4C23×C4111yescharacteristic
575C23×C4C23×C4111yescharacteristic
576C23×C4C23×C4111yescharacteristic
577C23×C4C23×C4111yescharacteristic
578C23×C4C23×C4111yescharacteristic
579C23×C4C23×C4111yescharacteristic
580C23×C4C23×C4111yescharacteristic
581C2×C4⋊C4—22no—
582C2×C4⋊C4—22no—
583C2×C4⋊C4—22no—
584C2×C4⋊C4—22no—
585C2×C4⋊C4—22no—
586C2×C4⋊C4—22no—
587C2×C4⋊C4—22no—
588C2×C4⋊C4—22no—
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—41no—
598C2×C4⋊C4C2×C4×C4114yes—
599C2×C4⋊C4C2×C4×C4114yes—
600C2×C4⋊C4C2×C4×C4114yes—
601C2×C4⋊C4D4×C4114yes—
602C2×C22⋊C4—22no—
603C2×C22⋊C4—22no—
604C2×C22⋊C4—22no—
605C2×C22⋊C4—22no—
606C2×C22⋊C4—22no—
607C2×C22⋊C4—22no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4—22no—
610C2×C22⋊C4—22no—
611C2×C22⋊C4—22no—
612C2×C22⋊C4—22no—
613C2×C22⋊C4—22no—
614C2×C22⋊C4—22no—
615C2×C22⋊C4—22no—
616C2×C22⋊C4—22no—
617C2×C22⋊C4—22no—
618C2×C22⋊C4—41no—
619C2×C22⋊C4—41no—
620C2×C22⋊C4C2×C4×C4114yes—
621C2×C22⋊C4C2×C4×C4114yes—
622C2×C22⋊C4C2×C4×C4114yes—
623C2×C42—22no—
624C2×C42—22no—
625C2×C42—22no—
626C2×C42—22no—
627C2×C42—22no—
628C2×C42—22no—
629C2×C42—22no—
630C2×C42—22no—
631C2×C42—22no—
632C2×C42—22no—
633C2×C42—22no—
634C2×C42—22no—
635C2×C42—41no—
636C2×C42—41no—
637C2×C42D4×C4114yes—
638#95—22no—
639#95—22no—
640#95—22no—
641#95—22no—
642#95—22no—
643#95—22no—
644#95—22no—
645#95—22no—
646#95—22no—
647#95—22no—
648#95—22no—
649#95—22no—
650#95—22no—
651#95—41no—
652#95C2×C4×C4114yes—
653#95D4×C4114yes—
654C24—21no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24—21no—
668C24C22×C4×C4112yes—
669C24C24×C4111yescharacteristic
670C22×C4—21no—
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×C4C22×C4×C4112yes—
747C22×C4C22×C4×C4112yes—
748C22×C4C22×C4×C4112yes—
749C22×C4C22×C4×C4112yes—
750C22×C4C22×C4×C4112yes—
751C22×C4C22×C4×C4112yes—
752C22×C4C2×D4×C4112yes—
753C22×C4C2×D4×C4112yes—
754C22×C4C2×D4×C4112yes—
755C22×C4C2×D4×C4112yes—
756C22×C4C2×D4×C4112yes—
757C22×C4C2×D4×C4112yes—
758C22×C4C2×D4×C4112yes—
759C22×C4C2×D4×C4112yes—
760C22×C4C2×D4×C4112yes—
761C22×C4#41×C4112yes—
762C22×C4#41×C4112yes—
763C22×C4#41×C4112yes—
764C22×C4#41×C4112yes—
765C22×C4#41×C4112yes—
766C22×C4#41×C4112yes—
767C22×C4#41×C4112yes—
768C4⋊C4—28no—
769C4⋊C4—28no—
770C4⋊C4—28no—
771C4⋊C4—28no—
772C4⋊C4—28no—
773C4⋊C4—44no—
774C4⋊C4—44no—
775C22⋊C4—28no—
776C22⋊C4—28no—
777C22⋊C4—28no—
778C22⋊C4—44no—
779C22⋊C4—44no—
780C22⋊C4—44no—
781C22⋊C4—44no—
782C42—28no—
783C42—28no—
784C42—44no—
785C42—44no—
786C42—44no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23C23×C4×C4111yescharacteristic
823C23C22×D4×C4111yescharacteristic
824C23C22×D4×C4111yescharacteristic
825C23C22×D4×C4111yescharacteristic
826C23C2×#41×C4111yescharacteristic
827C23C2×#41×C4111yescharacteristic
828C23C2×#41×C4111yescharacteristic
829C23C2×#41×C4111yescharacteristic
830C23C2×#41×C4111yescharacteristic
831C23C2×#41×C4111yescharacteristic
832C23C2×#41×C4111yescharacteristic
833C23H(5,𝔽2)×C4111yescharacteristic
834C232−1+4×C4111yescharacteristic
835C232−1+4×C4111yescharacteristic
836C232−1+4×C4111yescharacteristic
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
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—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
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×C4C4×D4×C4114yes—
931C2×C4C4×D4×C4114yes—
932C2×C4C4×D4×C4114yes—
933C2×C4#121×C4114yes—
934C2×C4#121×C4114yes—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22—42no—
941C22—42no—
942C22—81no—
943C22—81no—
944C22—81no—
945C22—81no—
946C22—81no—
947C22—81no—
948C22—81no—
949C22—81no—
950C22C2×C4×D4×C4111yescharacteristic
951C22C2×C4×D4×C4111yescharacteristic
952C22C2×C4×D4×C4111yescharacteristic
953C22C4×#41×C4111yescharacteristic
954C22C4×#41×C4111yescharacteristic
955C22C41×#51911yescharacteristic
956C22C41×#52011yescharacteristic
957C22C2×#121×C4111yescharacteristic
958C22C2×#121×C4111yescharacteristic
959C22C41×#52511yescharacteristic
960C22C41×#52511yescharacteristic
961C22C41×#52911yescharacteristic
962C22C41×#52911yescharacteristic
963C22C41×#53211yescharacteristic
964C22C41×#53211yescharacteristic
965C22C41×#53611yescharacteristic
966C22C41×#53711yescharacteristic
967C22C41×#54111yescharacteristic
968C22C41×#54211yescharacteristic
969C22D42×C4111yescharacteristic
970C22C41×#54711yescharacteristic
971C22C41×#54711yescharacteristic
972C22C41×#54711yescharacteristic
973C22C41×#54811yescharacteristic
974C22C41×#54811yescharacteristic
975C22C41×#54811yescharacteristic
976C22C41×#55111yescharacteristic
977C22C41×#55211yescharacteristic
978C22C41×#55211yescharacteristic
979C22C41×#55211yescharacteristic
980C22C41×#55311yescharacteristic
981C22C41×#55311yescharacteristic
982C22C41×#55611yescharacteristic
983C22C41×#55611yescharacteristic
984C22C41×#55611yescharacteristic
985C4—24no—
986C4—24no—
987C4—24no—
988C4—24no—
989C4—24no—
990C4—42no—
991C4—42no—
992C4—42no—
993C4—42no—
994C4—42no—
995C4—42no—
996C4—42no—
997C4—81no—
998C4—81no—
999C2—82no—
1000C2C4×#121×C4111yescharacteristic
1001C2C4×#121×C4111yescharacteristic
1002C2C41×#232311yescharacteristic
1003C2C41×#236111yescharacteristic
1004C2C41×#236211yescharacteristic
1005C2C41×#236211yescharacteristic
1006C2C41×#237311yescharacteristic
1007C2C41×#241311yescharacteristic
1008C2C41×#241611yescharacteristic
1009C2C41×#246111yescharacteristic
1010C2C41×#246911yescharacteristic
1011C2C41×#251911yescharacteristic
1012C2C41×#252511yescharacteristic
1013C2C41×#254511yescharacteristic
1014C2C41×#260111yescharacteristic
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
2. C2×C41×#389C2semidirect
6. C2×C4×C4⋊C4×C41C2semidirect
7. C2×C4×C4⋊C4×C41C2semidirect
8. C41×#1441C2semidirect
9. C41×#1441C2semidirect
13. C41×#1436C2semidirect
14. C41×#1436C2semidirect
15. C41×#1434C2semidirect
35. C41×#396C4semidirect
427. #14200C41direct (N × H)
493. C2×#389C2×C41semidirect
497. C2×C4×C4⋊C4C2×C41semidirect
498. C2×C4×C4⋊C4C2×C41semidirect
499. #1441C2×C41semidirect
500. #1441C2×C41semidirect
504. #1436C2×C41semidirect
505. #1436C2×C41semidirect
506. #1434C2×C41semidirect
542. #396C4×C41semidirect
565. C41#14200direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C41×#3962
C2×C41×#3892
C2×C41×#3882
C2×C4×C4⋊C4×C412
C41×#14412
C41×#14392
C41×#14372
C41×#14362
C41×#14342
#1420041