Finite Group Databasebeta

← C41×#22548 #23798749

Subgroups — C41×#22548 #23798749

Order 10496.

1054 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#556C211yesmaximal, characteristic
2C2×C41×#446C211yesmaximal, characteristic, complemented
3C41×#2355C211yesmaximal, characteristic, complemented
4C41×#1983C211yesmaximal, characteristic
5C41×#1983C211yesmaximal, characteristic
6C41×#1981C211yesmaximal, characteristic, complemented
7C41×#1960C211yesmaximal, characteristic, complemented
8C41×#1959C211yesmaximal, characteristic
9C41×#1958C211yesmaximal, characteristic
10C41×#1805C211yesmaximal, characteristic, complemented
11C41×#1804C211yesmaximal, characteristic
12C41×#1803C211yesmaximal, characteristic, complemented
13C41×#1763C211yesmaximal, characteristic, complemented
14C41×#1762C211yesmaximal, characteristic
15C4×#103×C41C211yesmaximal, characteristic, complemented
16C41×#556—24no—
17C41×#556C418yescomplemented
18C2×C4⋊Q8×C41C2211yescharacteristic
19C2×#126×C41—21no—
20C2×#126×C41—21no—
21C2×#124×C41C2211yescharacteristic
22C2×#124×C41C2211yescharacteristic
23C2×C22⋊Q8×C41—21no—
24C2×C4×Q8×C41C2211yescharacteristic
25C2×C4×Q8×C41C2211yescharacteristic
26C2×C4×Q8×C41C2211yescharacteristic
27C2×C4×D4×C41C2211yescharacteristic
28C2×#117×C41—21no—
29C41×#446—24no—
30C2×C4⋊C8×C41C2211yescharacteristic
31C2×C4⋊C8×C41C2211yescharacteristic
32C2×C4⋊C8×C41C2211yescharacteristic
33C2×#103×C41C2211yescharacteristic
34C2×#103×C41C2211yescharacteristic
35C2×#103×C41C2211yescharacteristic
36C2×#103×C41C2211yescharacteristic
37C2×#103×C41C2211yescharacteristic
38C2×#103×C41C2211yescharacteristic
39C2×#103×C41C2211yescharacteristic
40C2×#103×C41C2211yescharacteristic
41C2×#102×C41C2211yescharacteristic
42C2×#102×C41C2211yescharacteristic
43C2×#102×C41C2211yescharacteristic
44C2×#102×C41C2211yescharacteristic
45C2×#97×C41C2211yescharacteristic
46C2×#97×C41C2211yescharacteristic
47C2×C4×C8×C41C2211yescharacteristic
48C41×#391—21no—
49C41×#387—21no—
50C41×#387—21no—
51C41×#384C2211yescharacteristic
52C41×#382C2211yescharacteristic
53C41×#382C2211yescharacteristic
54C4×C4⋊C4×C41—21no—
55C4×C4⋊C4×C41C2211yescharacteristic
56C4×C4⋊C4×C41C2211yescharacteristic
57C4×C4⋊C4×C41C2211yescharacteristic
58C41×#340C2211yescharacteristic
59C41×#340C2211yescharacteristic
60C41×#340C2211yescharacteristic
61C41×#340C2211yescharacteristic
62C22×Q8×C41D411yescharacteristic
63C22×Q8×C41C2311yescharacteristic
64C22×Q8×C41C2311yescharacteristic
65C22×D4×C41C2311yescharacteristic
66C23×C4×C41—21no—
67C22×C8×C41C2311yescharacteristic
68C22×C8×C41C2311yescharacteristic
69C22×C8×C41C2311yescharacteristic
70C22×C8×C41C2311yescharacteristic
71C4⋊Q8×C41—22no—
72C4⋊Q8×C41C2×C414yes—
73#126×C41—28no—
74#126×C41—28no—
75#124×C41—22no—
76#124×C41—22no—
77#124×C41C2×C414yes—
78#124×C41C2×C414yes—
79C22⋊Q8×C41—28no—
80C4×Q8×C41—22no—
81C4×Q8×C41—22no—
82C4×Q8×C41C2×C414yes—
83C4×Q8×C41C2×C414yes—
84C4×Q8×C41C2×C414yes—
85C4×Q8×C41D414yes—
86C4×D4×C41—22no—
87C4×D4×C41C2×C414yes—
88#117×C41—28no—
89C2×C4⋊C4×C41—21no—
90C2×C4⋊C4×C41—21no—
91C2×C4⋊C4×C41—21no—
92C2×C4⋊C4×C41—21no—
93C2×C4⋊C4×C41—21no—
94C2×C4⋊C4×C41—21no—
95C2×C4⋊C4×C41D411yescharacteristic
96C2×C4⋊C4×C41D411yescharacteristic
97C2×C4⋊C4×C41D411yescharacteristic
98C2×C4⋊C4×C41C2311yescharacteristic
99C2×C4⋊C4×C41C2311yescharacteristic
100C2×C4⋊C4×C41C2311yescharacteristic
101C2×C4⋊C4×C41C2311yescharacteristic
102C2×C4⋊C4×C41C2311yescharacteristic
103C2×C22⋊C4×C41—21no—
104C2×C22⋊C4×C41—21no—
105C2×C22⋊C4×C41—21no—
106C2×C22⋊C4×C41—21no—
107C2×C22⋊C4×C41—21no—
108C2×C42×C41—21no—
109C2×C42×C41—21no—
110C2×C42×C41—21no—
111C2×C42×C41—21no—
112C2×C42×C41—21no—
113C2×C42×C41C2311yescharacteristic
114C2×C42×C41C2311yescharacteristic
115C2×C42×C41C2311yescharacteristic
116C4⋊C8×C41—22no—
117C4⋊C8×C41—22no—
118C4⋊C8×C41—22no—
119#103×C41—22no—
120#103×C41—22no—
121#103×C41—22no—
122#103×C41—22no—
123#103×C41—41no—
124#103×C41—41no—
125#103×C41—41no—
126#103×C41—41no—
127#102×C41—22no—
128#102×C41—22no—
129#102×C41—41no—
130#102×C41—41no—
131#97×C41—22no—
132#97×C41—22no—
133C4×C8×C41—22no—
134#95×C41—21no—
135#95×C41—21no—
136#95×C41—21no—
137#95×C41—21no—
138#95×C41—21no—
139#95×C41—21no—
140#95×C41—21no—
141C24×C41—21no—
142C2×Q8×C41—21no—
143C2×Q8×C41—21no—
144C2×Q8×C41—21no—
145C2×Q8×C41—21no—
146C2×Q8×C41—21no—
147C2×Q8×C41—21no—
148C2×Q8×C41—21no—
149C2×Q8×C41—21no—
150C2×Q8×C41—21no—
151C2×Q8×C41—21no—
152C2×Q8×C41—41no—
153C2×Q8×C41—41no—
154C2×Q8×C41C22⋊C414yes—
155C2×Q8×C41C22×C412yes—
156C2×Q8×C41C22×C412yes—
157C2×D4×C41—21no—
158C2×D4×C41—21no—
159C2×D4×C41—21no—
160C2×D4×C41—21no—
161C2×D4×C41—21no—
162C2×D4×C41C22×C412yes—
163C22×C4×C41—21no—
164C22×C4×C41—21no—
165C22×C4×C41—21no—
166C22×C4×C41—21no—
167C22×C4×C41—24no—
168C22×C4×C41—21no—
169C22×C4×C41—21no—
170C22×C4×C41—21no—
171C22×C4×C41—42no—
172C22×C4×C41—42no—
173C22×C4×C41C2×D411yescharacteristic
174C22×C4×C41C2×D411yescharacteristic
175C22×C4×C41C2×D411yescharacteristic
176C22×C4×C41C2×D411yescharacteristic
177C22×C4×C41C2×D411yescharacteristic
178C22×C4×C41C2×D411yescharacteristic
179C22×C4×C41C2411yescharacteristic
180C2×C8×C41—21no—
181C2×C8×C41—21no—
182C2×C8×C41—21no—
183C2×C8×C41—21no—
184C2×C8×C41—21no—
185C2×C8×C41—21no—
186C2×C8×C41—21no—
187C2×C8×C41—21no—
188C2×C8×C41—21no—
189C2×C8×C41—21no—
190C2×C8×C41—21no—
191C2×C8×C41#4112yes—
192C4⋊C4×C41—24no—
193C4⋊C4×C41—24no—
194C4⋊C4×C41—24no—
195C4⋊C4×C41—24no—
196C4⋊C4×C41—21no—
197C4⋊C4×C41—21no—
198C4⋊C4×C41—21no—
199C4⋊C4×C41—21no—
200C4⋊C4×C41—21no—
201C4⋊C4×C41—21no—
202C4⋊C4×C41—21no—
203C4⋊C4×C41—21no—
204C4⋊C4×C41—42no—
205C4⋊C4×C41—81no—
206C4⋊C4×C41C22⋊C414yes—
207C4⋊C4×C41C22⋊C414yes—
208C4⋊C4×C41C22⋊C414yes—
209C4⋊C4×C41C22×C412yes—
210C4⋊C4×C41#4112yes—
211C22⋊C4×C41—24no—
212C22⋊C4×C41—24no—
213C22⋊C4×C41—24no—
214C22⋊C4×C41—24no—
215C22⋊C4×C41—24no—
216C42×C41—24no—
217C42×C41—24no—
218C42×C41—42no—
219C42×C41—81no—
220C42×C41—81no—
221C42×C41C22×C412yes—
222C42×C41C22×C412yes—
223C42×C41C22×C412yes—
224C42×C41C2×D412yes—
225C42×C41C2×D412yes—
226C42×C41C2×D412yes—
227C23×C41—22no—
228C23×C41—41no—
229C23×C41—41no—
230C23×C41—41no—
231C23×C41—41no—
232C23×C41—41no—
233C23×C41—41no—
234C23×C41C22×D411yescharacteristic
235Q8×C41—22no—
236Q8×C41—22no—
237Q8×C41—22no—
238Q8×C41—22no—
239Q8×C41—44no—
240Q8×C41—41no—
241Q8×C41—41no—
242Q8×C41—41no—
243Q8×C41—41no—
244D4×C41—22no—
245D4×C41—22no—
246D4×C41—41no—
247D4×C41—41no—
248C2×C4×C41—21no—
249C2×C4×C41—21no—
250C2×C4×C41—21no—
251C2×C4×C41—21no—
252C2×C4×C41—21no—
253C2×C4×C41—21no—
254C2×C4×C41—21no—
255C2×C4×C41—21no—
256C2×C4×C41—21no—
257C2×C4×C41—21no—
258C2×C4×C41—21no—
259C2×C4×C41—21no—
260C2×C4×C41—22no—
261C2×C4×C41—22no—
262C2×C4×C41—22no—
263C2×C4×C41—22no—
264C2×C4×C41—48no—
265C2×C4×C41—41no—
266C2×C4×C41—41no—
267C2×C4×C41—41no—
268C2×C4×C41—41no—
269C2×C4×C41—41no—
270C2×C4×C41—41no—
271C2×C4×C41—41no—
272C2×C4×C41—41no—
273C2×C4×C41—41no—
274C2×C4×C41—41no—
275C2×C4×C41—41no—
276C2×C4×C41—41no—
277C2×C4×C41—41no—
278C2×C4×C41—41no—
279C2×C4×C41—41no—
280C2×C4×C41—41no—
281C2×C4×C41—41no—
282C2×C4×C41C2×C22⋊C412yes—
283C2×C4×C41C2×C22⋊C412yes—
284C2×C4×C41C2×C22⋊C412yes—
285C2×C4×C41C2×C22⋊C412yes—
286C2×C4×C41C2×C22⋊C412yes—
287C2×C4×C41C2×C22⋊C412yes—
288C2×C4×C41C23×C411yescharacteristic
289C2×C4×C41C22×D411yescharacteristic
290C2×C4×C41C2×#4111yescharacteristic
291C2×C4×C41C2×#4111yescharacteristic
292C2×C4×C41H(5,𝔽2)11yescharacteristic
293C2×C4×C412−1+411yescharacteristic
294C8×C41—22no—
295C8×C41—41no—
296C8×C41—41no—
297C8×C41—41no—
298#22548C4111yesmaximal, characteristic, direct product factor, Sylow
299C22×C41—42no—
300C22×C41—42no—
301C22×C41—42no—
302C22×C41—81no—
303C22×C41—81no—
304C22×C41—81no—
305C22×C41—81no—
306C22×C41C22×C22⋊C411yescharacteristic
307C22×C41#54811yescharacteristic
308C22×C41#55011yescharacteristic
309C22×C41#57511yescharacteristic
310C22×C41#57511yescharacteristic
311C22×C41#57711yescharacteristic
312C22×C41#57811yescharacteristic
313C4×C41—22no—
314C4×C41—22no—
315C4×C41—22no—
316C4×C41—22no—
317C4×C41—22no—
318C4×C41—22no—
319C4×C41—42no—
320C4×C41—42no—
321C4×C41—42no—
322C4×C41—42no—
323C4×C41—81no—
324C4×C41—81no—
325C4×C41—81no—
326C4×C41C4×#4111yescharacteristic
327C4×C41#52011yescharacteristic
328C4×C41#54811yescharacteristic
329C4×C41#55011yescharacteristic
330C2×#556C2×C4111yescharacteristic
331C2×#446C2×C4111yescharacteristic, complemented
332#2355C2×C4111yescharacteristic, complemented
333#1983C2×C4111yescharacteristic
334#1983C2×C4111yescharacteristic
335#1981C2×C4111yescharacteristic, complemented
336#1960C2×C4111yescharacteristic, complemented
337#1959C2×C4111yescharacteristic
338#1958C2×C4111yescharacteristic
339#1805C2×C4111yescharacteristic, complemented
340#1804C2×C4111yescharacteristic
341#1803C2×C4111yescharacteristic, complemented
342#1763C2×C4111yescharacteristic, complemented
343#1762C2×C4111yescharacteristic
344C4×#103C2×C4111yescharacteristic, complemented
345C2×C41—82no—
346C2×C41#234111yescharacteristic
347C2×C41#289611yescharacteristic
348C2×C41#289811yescharacteristic
349C2×C41#337611yescharacteristic
350C2×C41#337711yescharacteristic
351C2×C41#340111yescharacteristic
352C2×C41#340211yescharacteristic
353#556—24no—
354#556C4×C4118yescomplemented
355C2×C4⋊Q8C22×C4111yescharacteristic
356C2×#126—21no—
357C2×#126—21no—
358C2×#124C22×C4111yescharacteristic
359C2×#124C22×C4111yescharacteristic
360C2×C22⋊Q8—21no—
361C2×C4×Q8C22×C4111yescharacteristic
362C2×C4×Q8C22×C4111yescharacteristic
363C2×C4×Q8C22×C4111yescharacteristic
364C2×C4×D4C22×C4111yescharacteristic
365C2×#117—21no—
366#446—24no—
367C2×C4⋊C8C22×C4111yescharacteristic
368C2×C4⋊C8C22×C4111yescharacteristic
369C2×C4⋊C8C22×C4111yescharacteristic
370C2×#103C22×C4111yescharacteristic
371C2×#103C22×C4111yescharacteristic
372C2×#103C22×C4111yescharacteristic
373C2×#103C22×C4111yescharacteristic
374C2×#103C22×C4111yescharacteristic
375C2×#103C22×C4111yescharacteristic
376C2×#103C22×C4111yescharacteristic
377C2×#103C22×C4111yescharacteristic
378C2×#102C22×C4111yescharacteristic
379C2×#102C22×C4111yescharacteristic
380C2×#102C22×C4111yescharacteristic
381C2×#102C22×C4111yescharacteristic
382C2×#97C22×C4111yescharacteristic
383C2×#97C22×C4111yescharacteristic
384C2×C4×C8C22×C4111yescharacteristic
385#391—21no—
386#387—21no—
387#387—21no—
388#384C22×C4111yescharacteristic
389#382C22×C4111yescharacteristic
390#382C22×C4111yescharacteristic
391C4×C4⋊C4—21no—
392C4×C4⋊C4C22×C4111yescharacteristic
393C4×C4⋊C4C22×C4111yescharacteristic
394C4×C4⋊C4C22×C4111yescharacteristic
395#340C22×C4111yescharacteristic
396#340C22×C4111yescharacteristic
397#340C22×C4111yescharacteristic
398#340C22×C4111yescharacteristic
399C41#2254811yescharacteristic, direct product factor, Sylow
400C22×Q8D4×C4111yescharacteristic
401C22×Q8C23×C4111yescharacteristic
402C22×Q8C23×C4111yescharacteristic
403C22×D4C23×C4111yescharacteristic
404C23×C4—21no—
405C22×C8C23×C4111yescharacteristic
406C22×C8C23×C4111yescharacteristic
407C22×C8C23×C4111yescharacteristic
408C22×C8C23×C4111yescharacteristic
409C4⋊Q8—22no—
410C4⋊Q8C2×C4×C4114yes—
411#126—28no—
412#126—28no—
413#124—22no—
414#124—22no—
415#124C2×C4×C4114yes—
416#124C2×C4×C4114yes—
417C22⋊Q8—28no—
418C4×Q8—22no—
419C4×Q8—22no—
420C4×Q8C2×C4×C4114yes—
421C4×Q8C2×C4×C4114yes—
422C4×Q8C2×C4×C4114yes—
423C4×Q8D4×C4114yes—
424C4×D4—22no—
425C4×D4C2×C4×C4114yes—
426#117—28no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4D4×C4111yescharacteristic
434C2×C4⋊C4D4×C4111yescharacteristic
435C2×C4⋊C4D4×C4111yescharacteristic
436C2×C4⋊C4C23×C4111yescharacteristic
437C2×C4⋊C4C23×C4111yescharacteristic
438C2×C4⋊C4C23×C4111yescharacteristic
439C2×C4⋊C4C23×C4111yescharacteristic
440C2×C4⋊C4C23×C4111yescharacteristic
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C42—21no—
447C2×C42—21no—
448C2×C42—21no—
449C2×C42—21no—
450C2×C42—21no—
451C2×C42C23×C4111yescharacteristic
452C2×C42C23×C4111yescharacteristic
453C2×C42C23×C4111yescharacteristic
454C4⋊C8—22no—
455C4⋊C8—22no—
456C4⋊C8—22no—
457#103—22no—
458#103—22no—
459#103—22no—
460#103—22no—
461#103—41no—
462#103—41no—
463#103—41no—
464#103—41no—
465#102—22no—
466#102—22no—
467#102—41no—
468#102—41no—
469#97—22no—
470#97—22no—
471C4×C8—22no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95—21no—
476#95—21no—
477#95—21no—
478#95—21no—
479C24—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—41no—
491C2×Q8—41no—
492C2×Q8C22⋊C4×C4114yes—
493C2×Q8C22×C4×C4112yes—
494C2×Q8C22×C4×C4112yes—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4C22×C4×C4112yes—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—24no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4C2×D4×C4111yescharacteristic
512C22×C4C2×D4×C4111yescharacteristic
513C22×C4C2×D4×C4111yescharacteristic
514C22×C4C2×D4×C4111yescharacteristic
515C22×C4C2×D4×C4111yescharacteristic
516C22×C4C2×D4×C4111yescharacteristic
517C22×C4C24×C4111yescharacteristic
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8#41×C4112yes—
530C4⋊C4—24no—
531C4⋊C4—24no—
532C4⋊C4—24no—
533C4⋊C4—24no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—42no—
543C4⋊C4—81no—
544C4⋊C4C22⋊C4×C4114yes—
545C4⋊C4C22⋊C4×C4114yes—
546C4⋊C4C22⋊C4×C4114yes—
547C4⋊C4C22×C4×C4112yes—
548C4⋊C4#41×C4112yes—
549C22⋊C4—24no—
550C22⋊C4—24no—
551C22⋊C4—24no—
552C22⋊C4—24no—
553C22⋊C4—24no—
554C42—24no—
555C42—24no—
556C42—42no—
557C42—81no—
558C42—81no—
559C42C22×C4×C4112yes—
560C42C22×C4×C4112yes—
561C42C22×C4×C4112yes—
562C42C2×D4×C4112yes—
563C42C2×D4×C4112yes—
564C42C2×D4×C4112yes—
565C23—22no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23C22×D4×C4111yescharacteristic
573Q8—22no—
574Q8—22no—
575Q8—22no—
576Q8—22no—
577Q8—44no—
578Q8—41no—
579Q8—41no—
580Q8—41no—
581Q8—41no—
582D4—22no—
583D4—22no—
584D4—41no—
585D4—41no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—48no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4C2×C22⋊C4×C4112yes—
621C2×C4C2×C22⋊C4×C4112yes—
622C2×C4C2×C22⋊C4×C4112yes—
623C2×C4C2×C22⋊C4×C4112yes—
624C2×C4C2×C22⋊C4×C4112yes—
625C2×C4C2×C22⋊C4×C4112yes—
626C2×C4C23×C4×C4111yescharacteristic
627C2×C4C22×D4×C4111yescharacteristic
628C2×C4C2×#41×C4111yescharacteristic
629C2×C4C2×#41×C4111yescharacteristic
630C2×C4H(5,𝔽2)×C4111yescharacteristic
631C2×C42−1+4×C4111yescharacteristic
632C8—22no—
633C8—41no—
634C8—41no—
635C8—41no—
636C22—42no—
637C22—42no—
638C22—42no—
639C22—81no—
640C22—81no—
641C22—81no—
642C22—81no—
643C22C22×C22⋊C4×C4111yescharacteristic
644C22C41×#54811yescharacteristic
645C22C41×#55011yescharacteristic
646C22C41×#57511yescharacteristic
647C22C41×#57511yescharacteristic
648C22C41×#57711yescharacteristic
649C22C41×#57811yescharacteristic
650C4—22no—
651C4—22no—
652C4—22no—
653C4—22no—
654C4—22no—
655C4—22no—
656C4—42no—
657C4—42no—
658C4—42no—
659C4—42no—
660C4—81no—
661C4—81no—
662C4—81no—
663C4C4×#41×C4111yescharacteristic
664C4C41×#52011yescharacteristic
665C4C41×#54811yescharacteristic
666C4C41×#55011yescharacteristic
667C2—82no—
668C2C41×#234111yescharacteristic
669C2C41×#289611yescharacteristic
670C2C41×#289811yescharacteristic
671C2C41×#337611yescharacteristic
672C2C41×#337711yescharacteristic
673C2C41×#340111yescharacteristic
674C2C41×#340211yescharacteristic
subgroupG/H
center, socleC23×C41C22×D4
commutatorC2×C4C23×C4×C41
Frattini, cosocleC22×C4C24×C41
prime radicalC22×D4×C41C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C41 ◁ C2×C4×Q8×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C41×#446C2semidirect
3. C41×#2355C2semidirect
6. C41×#1981C2semidirect
7. C41×#1960C2semidirect
10. C41×#1805C2semidirect
12. C41×#1803C2semidirect
13. C41×#1763C2semidirect
15. C4×#103×C41C2semidirect
17. C41×#556C4semidirect
298. #22548C41direct (N × H)
331. C2×#446C2×C41semidirect
332. #2355C2×C41semidirect
335. #1981C2×C41semidirect
336. #1960C2×C41semidirect
339. #1805C2×C41semidirect
341. #1803C2×C41semidirect
342. #1763C2×C41semidirect
344. C4×#103C2×C41semidirect
354. #556C4×C41semidirect
399. C41#22548direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C41×#5562
C2×C41×#4462
C41×#23552
C41×#19832
C41×#19812
C41×#19602
C41×#19592
C41×#19582
C41×#18052
C41×#18042
C41×#18032
C41×#17632
C41×#17622
C4×#103×C412
#2254841