Finite Group Databasebeta

← C41×#23580 #23799781

Subgroups — C41×#23580 #23799781

Order 10496.

1242 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#540C211yesmaximal, characteristic, complemented
2C2×C41×#442C211yesmaximal, characteristic, complemented
3C2×C4×D8×C41C211yesmaximal, characteristic, complemented
4C41×#2324C211yesmaximal, characteristic, complemented
5C41×#2059C211yesmaximal, characteristic, complemented
6C41×#2041C211yesmaximal, characteristic, complemented
7C41×#2034C211yesmaximal, characteristic, complemented
8C41×#2033C211yesmaximal, characteristic, complemented
9C41×#2025C211yesmaximal, characteristic, complemented
10C41×#2011C211yesmaximal, characteristic, complemented
11C41×#1999C211yesmaximal, characteristic, complemented
12C41×#1999C211yesmaximal, characteristic, complemented
13C41×#1762C211yesmaximal, characteristic, complemented
14C4×#102×C41C211yesmaximal, characteristic, complemented
15C41×#1750C211yesmaximal, characteristic, complemented
16C22×D8×C41C2211yescharacteristic
17C22×D8×C41C2211yescharacteristic
18C41×#540—24no—
19C41×#540—24no—
20C2×#127×C41C2211yescharacteristic
21C2×#125×C41C2211yescharacteristic
22C2×#123×C41—21no—
23C2×#123×C41—21no—
24C2×#121×C41—21no—
25C2×#121×C41—21no—
26C2×#121×C41C2211yescharacteristic
27C2×#121×C41C2211yescharacteristic
28C2×#121×C41C2211yescharacteristic
29C2×C4×D4×C41C2211yescharacteristic
30C2×C4×D4×C41C2211yescharacteristic
31C2×C4×D4×C41C2211yescharacteristic
32C2×#117×C41C2211yescharacteristic
33C41×#442—24no—
34C4×D8×C41—24no—
35C2×#107×C41C2211yescharacteristic
36C2×#106×C41C2211yescharacteristic
37C2×#102×C41C2211yescharacteristic
38C2×#102×C41C2211yescharacteristic
39C2×#102×C41C2211yescharacteristic
40C2×#102×C41C2211yescharacteristic
41C2×#102×C41C2211yescharacteristic
42C2×#102×C41C2211yescharacteristic
43C2×#102×C41C2211yescharacteristic
44C2×#102×C41C2211yescharacteristic
45C2×C22⋊C8×C41C2211yescharacteristic
46C2×C22⋊C8×C41C2211yescharacteristic
47C2×#97×C41C2211yescharacteristic
48C2×C4×C8×C41C2211yescharacteristic
49C41×#390—21no—
50C41×#390C2211yescharacteristic
51C41×#389C2211yescharacteristic
52C41×#388—21no—
53C41×#386—21no—
54C41×#385—21no—
55C41×#380C2211yescharacteristic
56C4×C4⋊C4×C41C2211yescharacteristic
57C41×#340C2211yescharacteristic
58C41×#340C2211yescharacteristic
59C41×#340C2211yescharacteristic
60C41×#340C2211yescharacteristic
61C41×#336C2211yescharacteristic
62C41×#336C2211yescharacteristic
63C22×D4×C41—21no—
64C22×D4×C41—21no—
65C22×D4×C41—21no—
66C22×D4×C41—21no—
67C22×D4×C41—21no—
68C22×D4×C41C2311yescharacteristic
69C22×D4×C41C2311yescharacteristic
70C22×D4×C41C2311yescharacteristic
71C23×C4×C41—21no—
72C23×C4×C41—21no—
73C23×C4×C41—21no—
74C23×C4×C41C2311yescharacteristic
75C2×D8×C41—22no—
76C2×D8×C41—22no—
77C2×D8×C41—22no—
78C2×D8×C41—22no—
79C2×D8×C41—22no—
80C2×D8×C41—22no—
81C22×C8×C41C2311yescharacteristic
82C22×C8×C41C2311yescharacteristic
83C22×C8×C41C2311yescharacteristic
84C22×C8×C41C2311yescharacteristic
85#127×C41—22no—
86#127×C41—22no—
87#125×C41—22no—
88#125×C41—22no—
89#123×C41—28no—
90#123×C41—28no—
91#121×C41—28no—
92#121×C41—28no—
93#121×C41—22no—
94#121×C41—22no—
95#121×C41—22no—
96#121×C41—22no—
97#121×C41—22no—
98#121×C41—22no—
99C4×D4×C41—22no—
100C4×D4×C41—22no—
101C4×D4×C41—22no—
102C4×D4×C41—22no—
103C4×D4×C41D414yescomplemented
104C4×D4×C41D414yescomplemented
105#117×C41—22no—
106#117×C41—22no—
107C2×C4⋊C4×C41—21no—
108C2×C4⋊C4×C41—21no—
109C2×C4⋊C4×C41—21no—
110C2×C4⋊C4×C41D411yescharacteristic
111C2×C4⋊C4×C41D411yescharacteristic
112C2×C4⋊C4×C41C2311yescharacteristic
113C2×C4⋊C4×C41C2311yescharacteristic
114C2×C4⋊C4×C41C2311yescharacteristic
115C2×C4⋊C4×C41C2311yescharacteristic
116C2×C4⋊C4×C41C2311yescharacteristic
117C2×C22⋊C4×C41—21no—
118C2×C22⋊C4×C41—21no—
119C2×C22⋊C4×C41—21no—
120C2×C22⋊C4×C41—21no—
121C2×C22⋊C4×C41—21no—
122C2×C22⋊C4×C41—21no—
123C2×C22⋊C4×C41—21no—
124C2×C22⋊C4×C41—21no—
125C2×C22⋊C4×C41—21no—
126C2×C22⋊C4×C41D411yescharacteristic
127C2×C22⋊C4×C41D411yescharacteristic
128C2×C42×C41—21no—
129C2×C42×C41C2311yescharacteristic
130C2×C42×C41C2311yescharacteristic
131#107×C41—22no—
132#106×C41—22no—
133#102×C41—22no—
134#102×C41—22no—
135#102×C41—22no—
136#102×C41—22no—
137#102×C41—22no—
138#102×C41—22no—
139#102×C41—22no—
140#102×C41—22no—
141C22⋊C8×C41—22no—
142C22⋊C8×C41—22no—
143#97×C41—22no—
144C4×C8×C41—22no—
145#95×C41—21no—
146#95×C41—21no—
147#95×C41—21no—
148C24×C41—21no—
149C24×C41—21no—
150C24×C41—21no—
151C24×C41C2×D411yescharacteristic
152C2×D4×C41—24no—
153C2×D4×C41—24no—
154C2×D4×C41—24no—
155C2×D4×C41—24no—
156C2×D4×C41—24no—
157C2×D4×C41—21no—
158C2×D4×C41—21no—
159C2×D4×C41—21no—
160C2×D4×C41—21no—
161C2×D4×C41—21no—
162C2×D4×C41—21no—
163C2×D4×C41—21no—
164C2×D4×C41—21no—
165C2×D4×C41—21no—
166C2×D4×C41—21no—
167C2×D4×C41—21no—
168C2×D4×C41—21no—
169C2×D4×C41—21no—
170C2×D4×C41—21no—
171C2×D4×C41—21no—
172C2×D4×C41—81no—
173C2×D4×C41—81no—
174C2×D4×C41—81no—
175C2×D4×C41—81no—
176C2×D4×C41—81no—
177C2×D4×C41—81no—
178C2×D4×C41—81no—
179C2×D4×C41—81no—
180C2×D4×C41—81no—
181C2×D4×C41—81no—
182C2×D4×C41C2×D412yes—
183C2×D4×C41C2×D412yes—
184C2×D4×C41#4112yes—
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—24no—
195C22×C4×C41—24no—
196C22×C4×C41—21no—
197C22×C4×C41—21no—
198C22×C4×C41—42no—
199C22×C4×C41—81no—
200C22×C4×C41—81no—
201C22×C4×C41—81no—
202C22×C4×C41—81no—
203C22×C4×C41—81no—
204C22×C4×C41—81no—
205C22×C4×C41C2×D411yescharacteristic
206C22×C4×C41C2×D411yescharacteristic
207C22×C4×C41C2×D411yescharacteristic
208C22×C4×C41C2×D411yescharacteristic
209C22×C4×C41C2×D411yescharacteristic
210C22×C4×C41C2411yescharacteristic
211D8×C41—28no—
212D8×C41—28no—
213C2×C8×C41—21no—
214C2×C8×C41—21no—
215C2×C8×C41—21no—
216C2×C8×C41—21no—
217C2×C8×C41—21no—
218C2×C8×C41—21no—
219C2×C8×C41—21no—
220C2×C8×C41—21no—
221C2×C8×C41—21no—
222C2×C8×C41—21no—
223C2×C8×C41#4112yes—
224C2×C8×C41#4112yes—
225C4⋊C4×C41—24no—
226C4⋊C4×C41—24no—
227C4⋊C4×C41—22no—
228C4⋊C4×C41—22no—
229C4⋊C4×C41—21no—
230C4⋊C4×C41—21no—
231C4⋊C4×C41—21no—
232C4⋊C4×C41—21no—
233C4⋊C4×C41—21no—
234C4⋊C4×C41—21no—
235C4⋊C4×C41—21no—
236C4⋊C4×C41—81no—
237C4⋊C4×C41C2×D412yes—
238C4⋊C4×C41C2×D412yes—
239C4⋊C4×C41#4112yes—
240C22⋊C4×C41—24no—
241C22⋊C4×C41—24no—
242C22⋊C4×C41—24no—
243C22⋊C4×C41—24no—
244C22⋊C4×C41—24no—
245C22⋊C4×C41—22no—
246C22⋊C4×C41—22no—
247C22⋊C4×C41—42no—
248C22⋊C4×C41—81no—
249C22⋊C4×C41—81no—
250C22⋊C4×C41—81no—
251C42×C41—21no—
252C42×C41—21no—
253C42×C41—81no—
254C42×C41C2×D412yes—
255C42×C41C2×D412yes—
256C23×C41—21no—
257C23×C41—22no—
258C23×C41—22no—
259C23×C41—22no—
260C23×C41—21no—
261C23×C41—21no—
262C23×C41—21no—
263C23×C41—21no—
264C23×C41—21no—
265C23×C41—21no—
266C23×C41—41no—
267C23×C41—41no—
268C23×C41—41no—
269C23×C41—41no—
270C23×C41—41no—
271C23×C41—41no—
272C23×C41—41no—
273C23×C41—41no—
274C23×C41—41no—
275C23×C41—41no—
276C23×C41—41no—
277C23×C41—41no—
278C23×C41—41no—
279C23×C41—41no—
280C23×C41—41no—
281C23×C41—41no—
282C23×C41—41no—
283C23×C41—41no—
284C23×C41C22×D411yescharacteristic
285D4×C41—22no—
286D4×C41—22no—
287D4×C41—22no—
288D4×C41—22no—
289D4×C41—22no—
290D4×C41—22no—
291D4×C41—41no—
292D4×C41—41no—
293D4×C41—41no—
294D4×C41—41no—
295D4×C41—41no—
296D4×C41—41no—
297D4×C41—84no—
298D4×C41—84no—
299D4×C41—84no—
300D4×C41—84no—
301D4×C41—84no—
302C2×C4×C41—21no—
303C2×C4×C41—21no—
304C2×C4×C41—21no—
305C2×C4×C41—21no—
306C2×C4×C41—21no—
307C2×C4×C41—21no—
308C2×C4×C41—21no—
309C2×C4×C41—22no—
310C2×C4×C41—22no—
311C2×C4×C41—21no—
312C2×C4×C41—22no—
313C2×C4×C41—21no—
314C2×C4×C41—21no—
315C2×C4×C41—21no—
316C2×C4×C41—21no—
317C2×C4×C41—21no—
318C2×C4×C41—41no—
319C2×C4×C41—41no—
320C2×C4×C41—41no—
321C2×C4×C41—41no—
322C2×C4×C41—41no—
323C2×C4×C41—41no—
324C2×C4×C41—41no—
325C2×C4×C41—41no—
326C2×C4×C41—41no—
327C2×C4×C41—41no—
328C2×C4×C41—41no—
329C2×C4×C41—41no—
330C2×C4×C41—41no—
331C2×C4×C41—41no—
332C2×C4×C41—41no—
333C2×C4×C41—41no—
334C2×C4×C41—84no—
335C2×C4×C41—84no—
336C2×C4×C41—84no—
337C2×C4×C41#12012yes—
338C2×C4×C41#12012yes—
339C2×C4×C41C22×D411yescharacteristic
340C2×C4×C41C22×D411yescharacteristic
341C2×C4×C41C2×#4111yescharacteristic
342C2×C4×C41C2×#4111yescharacteristic
343C2×C4×C41C2×#4111yescharacteristic
344C2×C4×C41C2×#4111yescharacteristic
345C8×C41—22no—
346C8×C41—22no—
347C8×C41—41no—
348C8×C41—41no—
349#23580C4111yesmaximal, characteristic, direct product factor, Sylow
350C22×C41—41no—
351C22×C41—42no—
352C22×C41—41no—
353C22×C41—42no—
354C22×C41—41no—
355C22×C41—42no—
356C22×C41—42no—
357C22×C41—42no—
358C22×C41—41no—
359C22×C41—41no—
360C22×C41—42no—
361C22×C41—41no—
362C22×C41—42no—
363C22×C41—42no—
364C22×C41—41no—
365C22×C41—42no—
366C22×C41—81no—
367C22×C41—81no—
368C22×C41—81no—
369C22×C41—81no—
370C22×C41—81no—
371C22×C41—81no—
372C22×C41—81no—
373C22×C41—81no—
374C22×C41—81no—
375C22×C41—81no—
376C22×C41—81no—
377C22×C41—81no—
378C22×C41C2×#12011yescharacteristic
379C22×C41#52511yescharacteristic
380C22×C41#53211yescharacteristic
381C22×C41#57611yescharacteristic
382C22×C41#57611yescharacteristic
383C22×C41#57611yescharacteristic
384C22×C41#57711yescharacteristic
385C4×C41—22no—
386C4×C41—22no—
387C4×C41—42no—
388C4×C41—41no—
389C4×C41—41no—
390C4×C41—42no—
391C4×C41—41no—
392C4×C41—42no—
393C4×C41—81no—
394C4×C41—81no—
395C4×C41#52511yescharacteristic
396C4×C41#52511yescharacteristic
397C4×C41#53211yescharacteristic
398C4×C41#53211yescharacteristic
399C2×#540C2×C4111yescharacteristic, complemented
400C2×#442C2×C4111yescharacteristic, complemented
401C2×C4×D8C2×C4111yescharacteristic, complemented
402#2324C2×C4111yescharacteristic, complemented
403#2059C2×C4111yescharacteristic, complemented
404#2041C2×C4111yescharacteristic, complemented
405#2034C2×C4111yescharacteristic, complemented
406#2033C2×C4111yescharacteristic, complemented
407#2025C2×C4111yescharacteristic, complemented
408#2011C2×C4111yescharacteristic, complemented
409#1999C2×C4111yescharacteristic, complemented
410#1999C2×C4111yescharacteristic, complemented
411#1762C2×C4111yescharacteristic, complemented
412C4×#102C2×C4111yescharacteristic, complemented
413#1750C2×C4111yescharacteristic, complemented
414C2×C41—81no—
415C2×C41—82no—
416C2×C41—82no—
417C2×C41—82no—
418C2×C41#238811yescharacteristic
419C2×C41#300811yescharacteristic
420C2×C41#301211yescharacteristic
421C2×C41#311911yescharacteristic
422C2×C41#312211yescharacteristic
423C2×C41#317611yescharacteristic
424C2×C41#317911yescharacteristic
425C22×D8C22×C4111yescharacteristic
426C22×D8C22×C4111yescharacteristic
427#540—24no—
428#540—24no—
429C2×#127C22×C4111yescharacteristic
430C2×#125C22×C4111yescharacteristic
431C2×#123—21no—
432C2×#123—21no—
433C2×#121—21no—
434C2×#121—21no—
435C2×#121C22×C4111yescharacteristic
436C2×#121C22×C4111yescharacteristic
437C2×#121C22×C4111yescharacteristic
438C2×C4×D4C22×C4111yescharacteristic
439C2×C4×D4C22×C4111yescharacteristic
440C2×C4×D4C22×C4111yescharacteristic
441C2×#117C22×C4111yescharacteristic
442#442—24no—
443C4×D8—24no—
444C2×#107C22×C4111yescharacteristic
445C2×#106C22×C4111yescharacteristic
446C2×#102C22×C4111yescharacteristic
447C2×#102C22×C4111yescharacteristic
448C2×#102C22×C4111yescharacteristic
449C2×#102C22×C4111yescharacteristic
450C2×#102C22×C4111yescharacteristic
451C2×#102C22×C4111yescharacteristic
452C2×#102C22×C4111yescharacteristic
453C2×#102C22×C4111yescharacteristic
454C2×C22⋊C8C22×C4111yescharacteristic
455C2×C22⋊C8C22×C4111yescharacteristic
456C2×#97C22×C4111yescharacteristic
457C2×C4×C8C22×C4111yescharacteristic
458#390—21no—
459#390C22×C4111yescharacteristic
460#389C22×C4111yescharacteristic
461#388—21no—
462#386—21no—
463#385—21no—
464#380C22×C4111yescharacteristic
465C4×C4⋊C4C22×C4111yescharacteristic
466#340C22×C4111yescharacteristic
467#340C22×C4111yescharacteristic
468#340C22×C4111yescharacteristic
469#340C22×C4111yescharacteristic
470#336C22×C4111yescharacteristic
471#336C22×C4111yescharacteristic
472C41#2358011yescharacteristic, direct product factor, Sylow
473C22×D4—21no—
474C22×D4—21no—
475C22×D4—21no—
476C22×D4—21no—
477C22×D4—21no—
478C22×D4C23×C4111yescharacteristic
479C22×D4C23×C4111yescharacteristic
480C22×D4C23×C4111yescharacteristic
481C23×C4—21no—
482C23×C4—21no—
483C23×C4—21no—
484C23×C4C23×C4111yescharacteristic
485C2×D8—22no—
486C2×D8—22no—
487C2×D8—22no—
488C2×D8—22no—
489C2×D8—22no—
490C2×D8—22no—
491C22×C8C23×C4111yescharacteristic
492C22×C8C23×C4111yescharacteristic
493C22×C8C23×C4111yescharacteristic
494C22×C8C23×C4111yescharacteristic
495#127—22no—
496#127—22no—
497#125—22no—
498#125—22no—
499#123—28no—
500#123—28no—
501#121—28no—
502#121—28no—
503#121—22no—
504#121—22no—
505#121—22no—
506#121—22no—
507#121—22no—
508#121—22no—
509C4×D4—22no—
510C4×D4—22no—
511C4×D4—22no—
512C4×D4—22no—
513C4×D4D4×C4114yescomplemented
514C4×D4D4×C4114yescomplemented
515#117—22no—
516#117—22no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4D4×C4111yescharacteristic
521C2×C4⋊C4D4×C4111yescharacteristic
522C2×C4⋊C4C23×C4111yescharacteristic
523C2×C4⋊C4C23×C4111yescharacteristic
524C2×C4⋊C4C23×C4111yescharacteristic
525C2×C4⋊C4C23×C4111yescharacteristic
526C2×C4⋊C4C23×C4111yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4D4×C4111yescharacteristic
537C2×C22⋊C4D4×C4111yescharacteristic
538C2×C42—21no—
539C2×C42C23×C4111yescharacteristic
540C2×C42C23×C4111yescharacteristic
541#107—22no—
542#106—22no—
543#102—22no—
544#102—22no—
545#102—22no—
546#102—22no—
547#102—22no—
548#102—22no—
549#102—22no—
550#102—22no—
551C22⋊C8—22no—
552C22⋊C8—22no—
553#97—22no—
554C4×C8—22no—
555#95—21no—
556#95—21no—
557#95—21no—
558C24—21no—
559C24—21no—
560C24—21no—
561C24C2×D4×C4111yescharacteristic
562C2×D4—24no—
563C2×D4—24no—
564C2×D4—24no—
565C2×D4—24no—
566C2×D4—24no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—81no—
583C2×D4—81no—
584C2×D4—81no—
585C2×D4—81no—
586C2×D4—81no—
587C2×D4—81no—
588C2×D4—81no—
589C2×D4—81no—
590C2×D4—81no—
591C2×D4—81no—
592C2×D4C2×D4×C4112yes—
593C2×D4C2×D4×C4112yes—
594C2×D4#41×C4112yes—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—24no—
605C22×C4—24no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—42no—
609C22×C4—81no—
610C22×C4—81no—
611C22×C4—81no—
612C22×C4—81no—
613C22×C4—81no—
614C22×C4—81no—
615C22×C4C2×D4×C4111yescharacteristic
616C22×C4C2×D4×C4111yescharacteristic
617C22×C4C2×D4×C4111yescharacteristic
618C22×C4C2×D4×C4111yescharacteristic
619C22×C4C2×D4×C4111yescharacteristic
620C22×C4C24×C4111yescharacteristic
621D8—28no—
622D8—28no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8#41×C4112yes—
634C2×C8#41×C4112yes—
635C4⋊C4—24no—
636C4⋊C4—24no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—81no—
647C4⋊C4C2×D4×C4112yes—
648C4⋊C4C2×D4×C4112yes—
649C4⋊C4#41×C4112yes—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—24no—
653C22⋊C4—24no—
654C22⋊C4—24no—
655C22⋊C4—22no—
656C22⋊C4—22no—
657C22⋊C4—42no—
658C22⋊C4—81no—
659C22⋊C4—81no—
660C22⋊C4—81no—
661C42—21no—
662C42—21no—
663C42—81no—
664C42C2×D4×C4112yes—
665C42C2×D4×C4112yes—
666C23—21no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23C22×D4×C4111yescharacteristic
695D4—22no—
696D4—22no—
697D4—22no—
698D4—22no—
699D4—22no—
700D4—22no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—84no—
708D4—84no—
709D4—84no—
710D4—84no—
711D4—84no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—21no—
722C2×C4—22no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—84no—
745C2×C4—84no—
746C2×C4—84no—
747C2×C4#120×C4112yes—
748C2×C4#120×C4112yes—
749C2×C4C22×D4×C4111yescharacteristic
750C2×C4C22×D4×C4111yescharacteristic
751C2×C4C2×#41×C4111yescharacteristic
752C2×C4C2×#41×C4111yescharacteristic
753C2×C4C2×#41×C4111yescharacteristic
754C2×C4C2×#41×C4111yescharacteristic
755C8—22no—
756C8—22no—
757C8—41no—
758C8—41no—
759C22—41no—
760C22—42no—
761C22—41no—
762C22—42no—
763C22—41no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—41no—
768C22—41no—
769C22—42no—
770C22—41no—
771C22—42no—
772C22—42no—
773C22—41no—
774C22—42no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22C2×#120×C4111yescharacteristic
788C22C41×#52511yescharacteristic
789C22C41×#53211yescharacteristic
790C22C41×#57611yescharacteristic
791C22C41×#57611yescharacteristic
792C22C41×#57611yescharacteristic
793C22C41×#57711yescharacteristic
794C4—22no—
795C4—22no—
796C4—42no—
797C4—41no—
798C4—41no—
799C4—42no—
800C4—41no—
801C4—42no—
802C4—81no—
803C4—81no—
804C4C41×#52511yescharacteristic
805C4C41×#52511yescharacteristic
806C4C41×#53211yescharacteristic
807C4C41×#53211yescharacteristic
808C2—81no—
809C2—82no—
810C2—82no—
811C2—82no—
812C2C41×#238811yescharacteristic
813C2C41×#300811yescharacteristic
814C2C41×#301211yescharacteristic
815C2C41×#311911yescharacteristic
816C2C41×#312211yescharacteristic
817C2C41×#317611yescharacteristic
818C2C41×#317911yescharacteristic
subgroupG/H
center, socleC23×C41C22×D4
commutator, Frattini, cosocleC22×C4C24×C41
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C41 ◁ C2×#117×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C41×#540C2semidirect
2. C2×C41×#442C2semidirect
3. C2×C4×D8×C41C2semidirect
4. C41×#2324C2semidirect
5. C41×#2059C2semidirect
6. C41×#2041C2semidirect
7. C41×#2034C2semidirect
8. C41×#2033C2semidirect
9. C41×#2025C2semidirect
10. C41×#2011C2semidirect
11. C41×#1999C2semidirect
12. C41×#1999C2semidirect
13. C41×#1762C2semidirect
14. C4×#102×C41C2semidirect
15. C41×#1750C2semidirect
103. C4×D4×C41D4semidirect
104. C4×D4×C41D4semidirect
349. #23580C41direct (N × H)
399. C2×#540C2×C41semidirect
400. C2×#442C2×C41semidirect
401. C2×C4×D8C2×C41semidirect
402. #2324C2×C41semidirect
403. #2059C2×C41semidirect
404. #2041C2×C41semidirect
405. #2034C2×C41semidirect
406. #2033C2×C41semidirect
407. #2025C2×C41semidirect
408. #2011C2×C41semidirect
409. #1999C2×C41semidirect
410. #1999C2×C41semidirect
411. #1762C2×C41semidirect
412. C4×#102C2×C41semidirect
413. #1750C2×C41semidirect
472. C41#23580direct (N × H)
513. C4×D4D4×C41semidirect
514. C4×D4D4×C41semidirect

Maximal subgroups

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

subgroupindex
C2×C41×#5402
C2×C41×#4422
C2×C4×D8×C412
C41×#23242
C41×#20592
C41×#20412
C41×#20342
C41×#20332
C41×#20252
C41×#20112
C41×#19992
C41×#17622
C4×#102×C412
C41×#17502
#2358041