Finite Group Databasebeta

← C41×#14004 #23790205

Subgroups — C41×#14004 #23790205

Order 10496.

2106 conjugacy classes of subgroups.

The subgroup lattice has 1070 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#389C211yesmaximal, characteristic, complemented
2C2×C41×#385C211yesmaximal, characteristic
3C2×C41×#385C211yesmaximal, characteristic
4C2×C41×#385C211yesmaximal, characteristic
5C2×C41×#380C211yesmaximal, characteristic
6C2×C4×C22⋊C4×C41C211yesmaximal, characteristic
7C22×#95×C41C211yesmaximal, characteristic
8C41×#1444C211yesmaximal, characteristic, complemented
9C41×#1442C211yesmaximal, characteristic, complemented
10C41×#1441C211yesmaximal, characteristic, complemented
11C41×#1441C211yesmaximal, characteristic, complemented
12C41×#1436C211yesmaximal, characteristic, complemented
13C41×#1436C211yesmaximal, characteristic, complemented
14C41×C4⋊#95C211yesmaximal, characteristic, complemented
15C41×C22⋊#95C211yesmaximal, characteristic
16C24×C4×C41C2211yescharacteristic
17C24×C4×C41C2211yescharacteristic
18C24×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×C42×C41C2211yescharacteristic
32C22×C42×C41C2211yescharacteristic
33C41×#389—24no—
34C41×#385—24no—
35C41×#385—24no—
36C41×#385C418yescomplemented
37C41×#380—24no—
38C4×C22⋊C4×C41—24no—
39C2×#95×C41—24no—
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
56C2×#95×C41C2211yescharacteristic
57C2×#95×C41C2211yescharacteristic
58C25×C41C2311yescharacteristic
59C23×C4×C41—22no—
60C23×C4×C41—22no—
61C23×C4×C41—22no—
62C23×C4×C41—22no—
63C23×C4×C41—22no—
64C23×C4×C41—22no—
65C23×C4×C41—22no—
66C23×C4×C41—22no—
67C23×C4×C41—22no—
68C23×C4×C41—22no—
69C23×C4×C41—22no—
70C23×C4×C41—22no—
71C23×C4×C41—22no—
72C23×C4×C41—41no—
73C23×C4×C41—41no—
74C23×C4×C41—41no—
75C23×C4×C41—41no—
76C23×C4×C41—41no—
77C23×C4×C41—41no—
78C23×C4×C41C2×C414yes—
79C23×C4×C41Q814yes—
80C23×C4×C41C2311yescharacteristic
81C23×C4×C41C2311yescharacteristic
82C23×C4×C41C2311yescharacteristic
83C23×C4×C41C2311yescharacteristic
84C23×C4×C41C2311yescharacteristic
85C23×C4×C41C2311yescharacteristic
86C23×C4×C41C2311yescharacteristic
87C23×C4×C41C2311yescharacteristic
88C23×C4×C41C2311yescharacteristic
89C23×C4×C41C2311yescharacteristic
90C23×C4×C41C2311yescharacteristic
91C23×C4×C41C2311yescharacteristic
92C23×C4×C41C2311yescharacteristic
93C23×C4×C41C2311yescharacteristic
94C2×C4⋊C4×C41—22no—
95C2×C4⋊C4×C41—22no—
96C2×C4⋊C4×C41—22no—
97C2×C4⋊C4×C41—22no—
98C2×C4⋊C4×C41—22no—
99C2×C4⋊C4×C41—22no—
100C2×C4⋊C4×C41—22no—
101C2×C4⋊C4×C41—22no—
102C2×C4⋊C4×C41—22no—
103C2×C4⋊C4×C41—22no—
104C2×C4⋊C4×C41—22no—
105C2×C4⋊C4×C41—22no—
106C2×C4⋊C4×C41—22no—
107C2×C4⋊C4×C41—22no—
108C2×C4⋊C4×C41—41no—
109C2×C4⋊C4×C41—41no—
110C2×C4⋊C4×C41—41no—
111C2×C4⋊C4×C41—41no—
112C2×C4⋊C4×C41—41no—
113C2×C4⋊C4×C41—41no—
114C2×C4⋊C4×C41—41no—
115C2×C4⋊C4×C41—41no—
116C2×C4⋊C4×C41C2×C414yescomplemented
117C2×C4⋊C4×C41C2×C414yescomplemented
118C2×C22⋊C4×C41—22no—
119C2×C22⋊C4×C41—22no—
120C2×C22⋊C4×C41—22no—
121C2×C22⋊C4×C41—22no—
122C2×C22⋊C4×C41—22no—
123C2×C22⋊C4×C41—22no—
124C2×C22⋊C4×C41—22no—
125C2×C22⋊C4×C41C2×C414yes—
126C2×C22⋊C4×C41C2×C414yes—
127C2×C22⋊C4×C41D414yes—
128C2×C22⋊C4×C41D414yes—
129C2×C22⋊C4×C41Q814yes—
130C2×C42×C41—22no—
131C2×C42×C41—22no—
132C2×C42×C41—22no—
133C2×C42×C41—22no—
134C2×C42×C41—41no—
135C2×C42×C41—41no—
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—22no—
145#95×C41—22no—
146#95×C41—22no—
147#95×C41—22no—
148#95×C41—22no—
149#95×C41—41no—
150#95×C41—41no—
151#95×C41C2×C414yescomplemented
152#95×C41C2×C414yescomplemented
153#95×C41D414yes—
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×D412yes—
165C24×C41C2×Q812yes—
166C24×C41C2×Q812yes—
167C24×C41#4112yes—
168C24×C41#4112yes—
169C24×C41C2411yescharacteristic
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—28no—
187C22×C4×C41—28no—
188C22×C4×C41—28no—
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—28no—
238C22×C4×C41—28no—
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—21no—
247C22×C4×C41—21no—
248C22×C4×C41—21no—
249C22×C4×C41—21no—
250C22×C4×C41—21no—
251C22×C4×C41—21no—
252C22×C4×C41—21no—
253C22×C4×C41—44no—
254C22×C4×C41—44no—
255C22×C4×C41—44no—
256C22×C4×C41—44no—
257C22×C4×C41—44no—
258C22×C4×C41—44no—
259C22×C4×C41—44no—
260C22×C4×C41—44no—
261C22×C4×C41—44no—
262C22×C4×C41—44no—
263C22×C4×C41—44no—
264C22×C4×C41—44no—
265C22×C4×C41—44no—
266C22×C4×C41—44no—
267C22×C4×C41—44no—
268C22×C4×C41—44no—
269C22×C4×C41C22×C412yes—
270C22×C4×C41C22×C412yes—
271C22×C4×C41C22×C412yes—
272C22×C4×C41C22×C412yes—
273C22×C4×C41C22×C412yes—
274C22×C4×C41C22×C412yes—
275C22×C4×C41C2×D412yes—
276C22×C4×C41C2×D412yes—
277C22×C4×C41C2×D412yes—
278C22×C4×C41C2×D412yes—
279C22×C4×C41C2×D412yes—
280C22×C4×C41C2×D412yes—
281C22×C4×C41C2×D412yes—
282C22×C4×C41C2×Q812yes—
283C22×C4×C41C2×Q812yes—
284C22×C4×C41C2×Q812yes—
285C22×C4×C41C2×Q812yes—
286C22×C4×C41#4112yes—
287C22×C4×C41#4112yes—
288C22×C4×C41#4112yes—
289C4⋊C4×C41—28no—
290C4⋊C4×C41—44no—
291C4⋊C4×C41—44no—
292C4⋊C4×C41—44no—
293C4⋊C4×C41—44no—
294C4⋊C4×C41—44no—
295C4⋊C4×C41—44no—
296C4⋊C4×C41—44no—
297C22⋊C4×C41—28no—
298C22⋊C4×C41—28no—
299C22⋊C4×C41—44no—
300C22⋊C4×C41C4⋊C4116yescomplemented
301C42×C41—44no—
302C42×C41—44no—
303C23×C41—22no—
304C23×C41—22no—
305C23×C41—22no—
306C23×C41—22no—
307C23×C41—22no—
308C23×C41—22no—
309C23×C41—22no—
310C23×C41—22no—
311C23×C41—22no—
312C23×C41—22no—
313C23×C41—22no—
314C23×C41—22no—
315C23×C41—22no—
316C23×C41—22no—
317C23×C41—22no—
318C23×C41—22no—
319C23×C41—22no—
320C23×C41—22no—
321C23×C41—22no—
322C23×C41—22no—
323C23×C41—22no—
324C23×C41—22no—
325C23×C41—22no—
326C23×C41—22no—
327C23×C41—22no—
328C23×C41—22no—
329C23×C41—22no—
330C23×C41—22no—
331C23×C41C2×C4⋊C414yes—
332C23×C41C4×D414yes—
333C23×C41C4×Q814yes—
334C23×C41#12114yes—
335C23×C41C22⋊Q814yes—
336C23×C41#12514yes—
337C23×C41C4⋊Q814yes—
338C23×C41C23×C411yescharacteristic
339C23×C41C22×D411yescharacteristic
340C23×C41C22×D411yescharacteristic
341C23×C41C22×D411yescharacteristic
342C23×C41C22×Q811yescharacteristic
343C23×C41C22×Q811yescharacteristic
344C23×C41C2×#4111yescharacteristic
345C23×C41C2×#4111yescharacteristic
346C23×C41C2×#4111yescharacteristic
347C23×C41C2×#4111yescharacteristic
348C23×C41C2×#4111yescharacteristic
349C23×C41H(5,𝔽2)11yescharacteristic
350C23×C41H(5,𝔽2)11yescharacteristic
351C23×C41H(5,𝔽2)11yescharacteristic
352C23×C412−1+411yescharacteristic
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—22no—
382C2×C4×C41—22no—
383C2×C4×C41—22no—
384C2×C4×C41—22no—
385C2×C4×C41—22no—
386C2×C4×C41—22no—
387C2×C4×C41—22no—
388C2×C4×C41—22no—
389C2×C4×C41—22no—
390C2×C4×C41—22no—
391C2×C4×C41—22no—
392C2×C4×C41—22no—
393C2×C4×C41—22no—
394C2×C4×C41—22no—
395C2×C4×C41—22no—
396C2×C4×C41—22no—
397C2×C4×C41—22no—
398C2×C4×C41—22no—
399C2×C4×C41—22no—
400C2×C4×C41—22no—
401C2×C4×C41—416no—
402C2×C4×C41—416no—
403C2×C4×C41—416no—
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×C41—41no—
435C2×C4×C41—41no—
436C2×C4×C41—41no—
437C2×C4×C41—41no—
438C2×C4×C41—41no—
439C2×C4×C41—41no—
440C2×C4×C41—41no—
441C2×C4×C41—41no—
442C2×C4×C41—41no—
443C2×C4×C41—41no—
444C2×C4×C41—41no—
445C2×C4×C41—41no—
446C2×C4×C41—41no—
447C2×C4×C41—41no—
448C2×C4×C41—41no—
449C2×C4×C41—41no—
450C2×C4×C41C2×C4⋊C414yes—
451C2×C4×C41C2×C4⋊C414yes—
452C2×C4×C41C4×D414yes—
453C2×C4×C41C22⋊Q814yes—
454#14004C4111yesmaximal, characteristic, direct product factor, Sylow
455C22×C41—24no—
456C22×C41—24no—
457C22×C41—24no—
458C22×C41—24no—
459C22×C41—24no—
460C22×C41—24no—
461C22×C41—24no—
462C22×C41—24no—
463C22×C41—24no—
464C22×C41—24no—
465C22×C41—24no—
466C22×C41—24no—
467C22×C41—24no—
468C22×C41—24no—
469C22×C41#38918yescomplemented
470C22×C41C22×C4⋊C411yescharacteristic
471C22×C41C2×C4×D411yescharacteristic
472C22×C41C2×C4×D411yescharacteristic
473C22×C41C2×C4×Q811yescharacteristic
474C22×C41C4×#4111yescharacteristic
475C22×C41#51811yescharacteristic
476C22×C41#52011yescharacteristic
477C22×C41C2×#12111yescharacteristic
478C22×C41C2×C22⋊Q811yescharacteristic
479C22×C41C2×C22⋊Q811yescharacteristic
480C22×C41#52511yescharacteristic
481C22×C41C2×#12511yescharacteristic
482C22×C41#52911yescharacteristic
483C22×C41C2×C4⋊Q811yescharacteristic
484C22×C41#53311yescharacteristic
485C22×C41#53811yescharacteristic
486C22×C41#53911yescharacteristic
487C22×C41#54311yescharacteristic
488C22×C41#54411yescharacteristic
489C22×C41D4211yescharacteristic
490C22×C41D4211yescharacteristic
491C22×C41#54611yescharacteristic
492C22×C41#54611yescharacteristic
493C22×C41#54611yescharacteristic
494C22×C41#54611yescharacteristic
495C22×C41#54611yescharacteristic
496C22×C41#54711yescharacteristic
497C22×C41#54711yescharacteristic
498C22×C41D4×Q811yescharacteristic
499C22×C41#55111yescharacteristic
500C22×C41#55111yescharacteristic
501C22×C41#55211yescharacteristic
502C22×C41#55411yescharacteristic
503C22×C41#55411yescharacteristic
504C22×C41#55411yescharacteristic
505C4×C41—24no—
506C4×C41—24no—
507C4×C41—24no—
508C4×C41—24no—
509C4×C41—42no—
510C4×C41—42no—
511C4×C41—42no—
512C4×C41—42no—
513C4×C41—42no—
514C4×C41—42no—
515C4×C41—42no—
516C4×C41—42no—
517C4×C41—81no—
518C4×C41—81no—
519C2×#389C2×C4111yescharacteristic, complemented
520C2×#385C2×C4111yescharacteristic
521C2×#385C2×C4111yescharacteristic
522C2×#385C2×C4111yescharacteristic
523C2×#380C2×C4111yescharacteristic
524C2×C4×C22⋊C4C2×C4111yescharacteristic
525C22×#95C2×C4111yescharacteristic
526#1444C2×C4111yescharacteristic, complemented
527#1442C2×C4111yescharacteristic, complemented
528#1441C2×C4111yescharacteristic, complemented
529#1441C2×C4111yescharacteristic, complemented
530#1436C2×C4111yescharacteristic, complemented
531#1436C2×C4111yescharacteristic, complemented
532C4⋊#95C2×C4111yescharacteristic, complemented
533C22⋊#95C2×C4111yescharacteristic
534C2×C41—28no—
535C2×C41C2×#38911yescharacteristic
536C2×C41C4×C22⋊Q811yescharacteristic
537C2×C41#232911yescharacteristic
538C2×C41D4×C4⋊C411yescharacteristic
539C2×C41#234911yescharacteristic
540C2×C41#235811yescharacteristic
541C2×C41#235911yescharacteristic
542C2×C41#242411yescharacteristic
543C2×C41#242511yescharacteristic
544C2×C41#243711yescharacteristic
545C2×C41#243811yescharacteristic
546C2×C41#244011yescharacteristic
547C2×C41#247311yescharacteristic
548C2×C41#250511yescharacteristic
549C2×C41#254911yescharacteristic
550C24×C4C22×C4111yescharacteristic
551C24×C4C22×C4111yescharacteristic
552C24×C4C22×C4111yescharacteristic
553C22×C4⋊C4C22×C4111yescharacteristic
554C22×C4⋊C4C22×C4111yescharacteristic
555C22×C4⋊C4C22×C4111yescharacteristic
556C22×C4⋊C4C22×C4111yescharacteristic
557C22×C4⋊C4C22×C4111yescharacteristic
558C22×C4⋊C4C22×C4111yescharacteristic
559C22×C4⋊C4C22×C4111yescharacteristic
560C22×C4⋊C4C22×C4111yescharacteristic
561C22×C22⋊C4C22×C4111yescharacteristic
562C22×C22⋊C4C22×C4111yescharacteristic
563C22×C22⋊C4C22×C4111yescharacteristic
564C22×C22⋊C4C22×C4111yescharacteristic
565C22×C42C22×C4111yescharacteristic
566C22×C42C22×C4111yescharacteristic
567#389—24no—
568#385—24no—
569#385—24no—
570#385C4×C4118yescomplemented
571#380—24no—
572C4×C22⋊C4—24no—
573C2×#95—24no—
574C2×#95C22×C4111yescharacteristic
575C2×#95C22×C4111yescharacteristic
576C2×#95C22×C4111yescharacteristic
577C2×#95C22×C4111yescharacteristic
578C2×#95C22×C4111yescharacteristic
579C2×#95C22×C4111yescharacteristic
580C2×#95C22×C4111yescharacteristic
581C2×#95C22×C4111yescharacteristic
582C2×#95C22×C4111yescharacteristic
583C2×#95C22×C4111yescharacteristic
584C2×#95C22×C4111yescharacteristic
585C2×#95C22×C4111yescharacteristic
586C2×#95C22×C4111yescharacteristic
587C2×#95C22×C4111yescharacteristic
588C2×#95C22×C4111yescharacteristic
589C2×#95C22×C4111yescharacteristic
590C2×#95C22×C4111yescharacteristic
591C2×#95C22×C4111yescharacteristic
592C41#1400411yescharacteristic, direct product factor, Sylow
593C25C23×C4111yescharacteristic
594C23×C4—22no—
595C23×C4—22no—
596C23×C4—22no—
597C23×C4—22no—
598C23×C4—22no—
599C23×C4—22no—
600C23×C4—22no—
601C23×C4—22no—
602C23×C4—22no—
603C23×C4—22no—
604C23×C4—22no—
605C23×C4—22no—
606C23×C4—22no—
607C23×C4—41no—
608C23×C4—41no—
609C23×C4—41no—
610C23×C4—41no—
611C23×C4—41no—
612C23×C4—41no—
613C23×C4C2×C4×C4114yes—
614C23×C4Q8×C4114yes—
615C23×C4C23×C4111yescharacteristic
616C23×C4C23×C4111yescharacteristic
617C23×C4C23×C4111yescharacteristic
618C23×C4C23×C4111yescharacteristic
619C23×C4C23×C4111yescharacteristic
620C23×C4C23×C4111yescharacteristic
621C23×C4C23×C4111yescharacteristic
622C23×C4C23×C4111yescharacteristic
623C23×C4C23×C4111yescharacteristic
624C23×C4C23×C4111yescharacteristic
625C23×C4C23×C4111yescharacteristic
626C23×C4C23×C4111yescharacteristic
627C23×C4C23×C4111yescharacteristic
628C23×C4C23×C4111yescharacteristic
629C2×C4⋊C4—22no—
630C2×C4⋊C4—22no—
631C2×C4⋊C4—22no—
632C2×C4⋊C4—22no—
633C2×C4⋊C4—22no—
634C2×C4⋊C4—22no—
635C2×C4⋊C4—22no—
636C2×C4⋊C4—22no—
637C2×C4⋊C4—22no—
638C2×C4⋊C4—22no—
639C2×C4⋊C4—22no—
640C2×C4⋊C4—22no—
641C2×C4⋊C4—22no—
642C2×C4⋊C4—22no—
643C2×C4⋊C4—41no—
644C2×C4⋊C4—41no—
645C2×C4⋊C4—41no—
646C2×C4⋊C4—41no—
647C2×C4⋊C4—41no—
648C2×C4⋊C4—41no—
649C2×C4⋊C4—41no—
650C2×C4⋊C4—41no—
651C2×C4⋊C4C2×C4×C4114yescomplemented
652C2×C4⋊C4C2×C4×C4114yescomplemented
653C2×C22⋊C4—22no—
654C2×C22⋊C4—22no—
655C2×C22⋊C4—22no—
656C2×C22⋊C4—22no—
657C2×C22⋊C4—22no—
658C2×C22⋊C4—22no—
659C2×C22⋊C4—22no—
660C2×C22⋊C4C2×C4×C4114yes—
661C2×C22⋊C4C2×C4×C4114yes—
662C2×C22⋊C4D4×C4114yes—
663C2×C22⋊C4D4×C4114yes—
664C2×C22⋊C4Q8×C4114yes—
665C2×C42—22no—
666C2×C42—22no—
667C2×C42—22no—
668C2×C42—22no—
669C2×C42—41no—
670C2×C42—41no—
671#95—22no—
672#95—22no—
673#95—22no—
674#95—22no—
675#95—22no—
676#95—22no—
677#95—22no—
678#95—22no—
679#95—22no—
680#95—22no—
681#95—22no—
682#95—22no—
683#95—22no—
684#95—41no—
685#95—41no—
686#95C2×C4×C4114yescomplemented
687#95C2×C4×C4114yescomplemented
688#95D4×C4114yes—
689C24—21no—
690C24—21no—
691C24—21no—
692C24—21no—
693C24—21no—
694C24—21no—
695C24—21no—
696C24—21no—
697C24C22×C4×C4112yes—
698C24C2×D4×C4112yes—
699C24C2×D4×C4112yes—
700C24C2×Q8×C4112yes—
701C24C2×Q8×C4112yes—
702C24#41×C4112yes—
703C24#41×C4112yes—
704C24C24×C4111yescharacteristic
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—28no—
722C22×C4—28no—
723C22×C4—28no—
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—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—28no—
773C22×C4—28no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—44no—
789C22×C4—44no—
790C22×C4—44no—
791C22×C4—44no—
792C22×C4—44no—
793C22×C4—44no—
794C22×C4—44no—
795C22×C4—44no—
796C22×C4—44no—
797C22×C4—44no—
798C22×C4—44no—
799C22×C4—44no—
800C22×C4—44no—
801C22×C4—44no—
802C22×C4—44no—
803C22×C4—44no—
804C22×C4C22×C4×C4112yes—
805C22×C4C22×C4×C4112yes—
806C22×C4C22×C4×C4112yes—
807C22×C4C22×C4×C4112yes—
808C22×C4C22×C4×C4112yes—
809C22×C4C22×C4×C4112yes—
810C22×C4C2×D4×C4112yes—
811C22×C4C2×D4×C4112yes—
812C22×C4C2×D4×C4112yes—
813C22×C4C2×D4×C4112yes—
814C22×C4C2×D4×C4112yes—
815C22×C4C2×D4×C4112yes—
816C22×C4C2×D4×C4112yes—
817C22×C4C2×Q8×C4112yes—
818C22×C4C2×Q8×C4112yes—
819C22×C4C2×Q8×C4112yes—
820C22×C4C2×Q8×C4112yes—
821C22×C4#41×C4112yes—
822C22×C4#41×C4112yes—
823C22×C4#41×C4112yes—
824C4⋊C4—28no—
825C4⋊C4—44no—
826C4⋊C4—44no—
827C4⋊C4—44no—
828C4⋊C4—44no—
829C4⋊C4—44no—
830C4⋊C4—44no—
831C4⋊C4—44no—
832C22⋊C4—28no—
833C22⋊C4—28no—
834C22⋊C4—44no—
835C22⋊C4C4⋊C4×C41116yescomplemented
836C42—44no—
837C42—44no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—22no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23C2×C4⋊C4×C4114yes—
867C23C4×D4×C4114yes—
868C23C4×Q8×C4114yes—
869C23#121×C4114yes—
870C23C22⋊Q8×C4114yes—
871C23#125×C4114yes—
872C23C4⋊Q8×C4114yes—
873C23C23×C4×C4111yescharacteristic
874C23C22×D4×C4111yescharacteristic
875C23C22×D4×C4111yescharacteristic
876C23C22×D4×C4111yescharacteristic
877C23C22×Q8×C4111yescharacteristic
878C23C22×Q8×C4111yescharacteristic
879C23C2×#41×C4111yescharacteristic
880C23C2×#41×C4111yescharacteristic
881C23C2×#41×C4111yescharacteristic
882C23C2×#41×C4111yescharacteristic
883C23C2×#41×C4111yescharacteristic
884C23H(5,𝔽2)×C4111yescharacteristic
885C23H(5,𝔽2)×C4111yescharacteristic
886C23H(5,𝔽2)×C4111yescharacteristic
887C232−1+4×C4111yescharacteristic
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—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—416no—
937C2×C4—416no—
938C2×C4—416no—
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×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4C2×C4⋊C4×C4114yes—
986C2×C4C2×C4⋊C4×C4114yes—
987C2×C4C4×D4×C4114yes—
988C2×C4C22⋊Q8×C4114yes—
989C22—24no—
990C22—24no—
991C22—24no—
992C22—24no—
993C22—24no—
994C22—24no—
995C22—24no—
996C22—24no—
997C22—24no—
998C22—24no—
999C22—24no—
1000C22—24no—
1001C22—24no—
1002C22—24no—
1003C22C41×#38918yescomplemented
1004C22C22×C4⋊C4×C4111yescharacteristic
1005C22C2×C4×D4×C4111yescharacteristic
1006C22C2×C4×D4×C4111yescharacteristic
1007C22C2×C4×Q8×C4111yescharacteristic
1008C22C4×#41×C4111yescharacteristic
1009C22C41×#51811yescharacteristic
1010C22C41×#52011yescharacteristic
1011C22C2×#121×C4111yescharacteristic
1012C22C2×C22⋊Q8×C4111yescharacteristic
1013C22C2×C22⋊Q8×C4111yescharacteristic
1014C22C41×#52511yescharacteristic
1015C22C2×#125×C4111yescharacteristic
1016C22C41×#52911yescharacteristic
1017C22C2×C4⋊Q8×C4111yescharacteristic
1018C22C41×#53311yescharacteristic
1019C22C41×#53811yescharacteristic
1020C22C41×#53911yescharacteristic
1021C22C41×#54311yescharacteristic
1022C22C41×#54411yescharacteristic
1023C22D42×C4111yescharacteristic
1024C22D42×C4111yescharacteristic
1025C22C41×#54611yescharacteristic
1026C22C41×#54611yescharacteristic
1027C22C41×#54611yescharacteristic
1028C22C41×#54611yescharacteristic
1029C22C41×#54611yescharacteristic
1030C22C41×#54711yescharacteristic
1031C22C41×#54711yescharacteristic
1032C22D4×Q8×C4111yescharacteristic
1033C22C41×#55111yescharacteristic
1034C22C41×#55111yescharacteristic
1035C22C41×#55211yescharacteristic
1036C22C41×#55411yescharacteristic
1037C22C41×#55411yescharacteristic
1038C22C41×#55411yescharacteristic
1039C4—24no—
1040C4—24no—
1041C4—24no—
1042C4—24no—
1043C4—42no—
1044C4—42no—
1045C4—42no—
1046C4—42no—
1047C4—42no—
1048C4—42no—
1049C4—42no—
1050C4—42no—
1051C4—81no—
1052C4—81no—
1053C2—28no—
1054C2C2×C41×#38911yescharacteristic
1055C2C4×C22⋊Q8×C4111yescharacteristic
1056C2C41×#232911yescharacteristic
1057C2D4×C4⋊C4×C4111yescharacteristic
1058C2C41×#234911yescharacteristic
1059C2C41×#235811yescharacteristic
1060C2C41×#235911yescharacteristic
1061C2C41×#242411yescharacteristic
1062C2C41×#242511yescharacteristic
1063C2C41×#243711yescharacteristic
1064C2C41×#243811yescharacteristic
1065C2C41×#244011yescharacteristic
1066C2C41×#247311yescharacteristic
1067C2C41×#250511yescharacteristic
1068C2C41×#254911yescharacteristic
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
8. C41×#1444C2semidirect
9. C41×#1442C2semidirect
10. C41×#1441C2semidirect
11. C41×#1441C2semidirect
12. C41×#1436C2semidirect
13. C41×#1436C2semidirect
14. C41×C4⋊#95C2semidirect
36. C41×#385C4semidirect
116. C2×C4⋊C4×C41C2×C4semidirect
117. C2×C4⋊C4×C41C2×C4semidirect
151. #95×C41C2×C4semidirect
152. #95×C41C2×C4semidirect
300. C22⋊C4×C41C4⋊C4semidirect
454. #14004C41direct (N × H)
469. C22×C41#389semidirect
519. C2×#389C2×C41semidirect
526. #1444C2×C41semidirect
527. #1442C2×C41semidirect
528. #1441C2×C41semidirect
529. #1441C2×C41semidirect
530. #1436C2×C41semidirect
531. #1436C2×C41semidirect
532. C4⋊#95C2×C41semidirect
570. #385C4×C41semidirect
592. C41#14004direct (N × H)
651. C2×C4⋊C4C2×C4×C41semidirect
652. C2×C4⋊C4C2×C4×C41semidirect
686. #95C2×C4×C41semidirect
687. #95C2×C4×C41semidirect
835. C22⋊C4C4⋊C4×C41semidirect
1003. C22C41×#389semidirect

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×#3852
C2×C41×#3802
C2×C4×C22⋊C4×C412
C22×#95×C412
C41×#14442
C41×#14422
C41×#14412
C41×#14362
C41×C4⋊#952
C41×C22⋊#952
#1400441