Finite Group Databasebeta

← C41×#25553 #23801754

Subgroups — C41×#25553 #23801754

Order 10496.

1200 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#553C211yesmaximal, characteristic, complemented
2C2×C41×#480C211yesmaximal, characteristic, complemented
3C2×C41×#469C211yesmaximal, characteristic, complemented
4C41×#2414C211yesmaximal, characteristic, complemented
5C41×#2059C211yesmaximal, characteristic, complemented
6C41×#2033C211yesmaximal, characteristic, complemented
7C41×#2025C211yesmaximal, characteristic, complemented
8C41×#1999C211yesmaximal, characteristic, complemented
9C41×#1879C211yesmaximal, characteristic, complemented
10C41×#1875C211yesmaximal, characteristic, complemented
11C41×#1875C211yesmaximal, characteristic, complemented
12C41×#1870C211yesmaximal, characteristic, complemented
13C41×#1862C211yesmaximal, characteristic, complemented
14C41×#1854C211yesmaximal, characteristic, complemented
15C41×#1736C211yesmaximal, characteristic, complemented
16C22×D8×C41C2211yescharacteristic
17C22×M16×C41C2211yescharacteristic
18C41×#553—24no—
19C41×#553—24no—
20C2×#126×C41—21no—
21C2×#125×C41C2211yescharacteristic
22C2×#123×C41—21no—
23C2×#121×C41—21no—
24C2×#121×C41C2211yescharacteristic
25C2×#121×C41C2211yescharacteristic
26C2×#121×C41C2211yescharacteristic
27C2×#121×C41C2211yescharacteristic
28C2×C4×D4×C41—21no—
29C2×C4×D4×C41C2211yescharacteristic
30C2×C4×D4×C41C2211yescharacteristic
31C2×#117×C41C2211yescharacteristic
32C2×#117×C41C2211yescharacteristic
33C22×C4⋊C4×C41C2211yescharacteristic
34C41×#480—24no—
35C41×#469—24no—
36C2×#107×C41C2211yescharacteristic
37C2×#107×C41C2211yescharacteristic
38C2×#106×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×C22⋊C8×C41C2211yescharacteristic
48C41×#394—21no—
49C41×#392—21no—
50C41×#390—21no—
51C41×#390C2211yescharacteristic
52C41×#389C2211yescharacteristic
53C41×#388—21no—
54C41×#380C2211yescharacteristic
55C41×#340C2211yescharacteristic
56C41×#340C2211yescharacteristic
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×C41D411yescharacteristic
68C22×D4×C41C2311yescharacteristic
69C22×D4×C41C2311yescharacteristic
70C23×C4×C41—21no—
71C23×C4×C41—21no—
72C23×C4×C41C2311yescharacteristic
73C23×C4×C41C2311yescharacteristic
74C2×D8×C41—22no—
75C2×D8×C41—22no—
76C2×D8×C41—41no—
77C2×M16×C41—22no—
78C2×M16×C41—22no—
79C2×M16×C41—41no—
80C22×C8×C41C2311yescharacteristic
81C22×C8×C41C2311yescharacteristic
82C22×C8×C41C2311yescharacteristic
83C22×C8×C41C2311yescharacteristic
84#126×C41—28no—
85#125×C41—22no—
86#125×C41—22no—
87#123×C41—28no—
88#121×C41—28no—
89#121×C41—22no—
90#121×C41—22no—
91#121×C41—22no—
92#121×C41—22no—
93#121×C41—22no—
94#121×C41—22no—
95#121×C41—41no—
96#121×C41D414yescomplemented
97C4×D4×C41—28no—
98C4×D4×C41—22no—
99C4×D4×C41—22no—
100C4×D4×C41—22no—
101C4×D4×C41—22no—
102#117×C41—22no—
103#117×C41—22no—
104#117×C41—22no—
105#117×C41—41no—
106C2×C4⋊C4×C41—21no—
107C2×C4⋊C4×C41—22no—
108C2×C4⋊C4×C41—21no—
109C2×C4⋊C4×C41—21no—
110C2×C4⋊C4×C41—21no—
111C2×C4⋊C4×C41D411yescharacteristic
112C2×C4⋊C4×C41D414yescomplemented
113C2×C4⋊C4×C41C2311yescharacteristic
114C2×C4⋊C4×C41C2311yescharacteristic
115C2×C4⋊C4×C41C2311yescharacteristic
116C2×C4⋊C4×C41C2311yescharacteristic
117C2×C4⋊C4×C41C2311yescharacteristic
118C2×C4⋊C4×C41C2311yescharacteristic
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×C41—21no—
127C2×C22⋊C4×C41—21no—
128C2×C22⋊C4×C41—21no—
129C2×C22⋊C4×C41D411yescharacteristic
130C2×C22⋊C4×C41D411yescharacteristic
131C2×C42×C41—21no—
132C2×C42×C41—21no—
133C2×C42×C41C2311yescharacteristic
134#107×C41—22no—
135#107×C41—22no—
136#106×C41—22no—
137#102×C41—22no—
138#102×C41—22no—
139#102×C41—22no—
140#102×C41—22no—
141#102×C41—22no—
142#102×C41—41no—
143C22⋊C8×C41—22no—
144C22⋊C8×C41—22no—
145C22⋊C8×C41—41no—
146#95×C41—21no—
147#95×C41—21no—
148C24×C41—21no—
149C24×C41—21no—
150C24×C41C2×D411yescharacteristic
151C24×C41C2×D411yescharacteristic
152C2×D4×C41—22no—
153C2×D4×C41—24no—
154C2×D4×C41—24no—
155C2×D4×C41—21no—
156C2×D4×C41—21no—
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—41no—
167C2×D4×C41—41no—
168C2×D4×C41—42no—
169C2×D4×C41—42no—
170C2×D4×C41—42no—
171C2×D4×C41—42no—
172C2×D4×C41—42no—
173C2×D4×C41—81no—
174C2×D4×C41—81no—
175C2×D4×C41—81no—
176C2×D4×C41—81no—
177C2×D4×C41—81no—
178C2×D4×C41C2×D412yes—
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—24no—
188C22×C4×C41—24no—
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—81no—
198C22×C4×C41—81no—
199C22×C4×C41—81no—
200C22×C4×C41—81no—
201C22×C4×C41C2×D411yescharacteristic
202C22×C4×C41C2×D411yescharacteristic
203C22×C4×C41C2×D411yescharacteristic
204C22×C4×C41C2×D411yescharacteristic
205C22×C4×C41C2×D412yes—
206C22×C4×C41C2×D412yes—
207C22×C4×C41C2411yescharacteristic
208D8×C41—44no—
209M16×C41—44no—
210C2×C8×C41—21no—
211C2×C8×C41—21no—
212C2×C8×C41—21no—
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#4112yes—
222C4⋊C4×C41—24no—
223C4⋊C4×C41—24no—
224C4⋊C4×C41—24no—
225C4⋊C4×C41—22no—
226C4⋊C4×C41—21no—
227C4⋊C4×C41—21no—
228C4⋊C4×C41—21no—
229C4⋊C4×C41—21no—
230C4⋊C4×C41—21no—
231C4⋊C4×C41—21no—
232C4⋊C4×C41—21no—
233C4⋊C4×C41—21no—
234C4⋊C4×C41—81no—
235C4⋊C4×C41C2×D412yes—
236C4⋊C4×C41C2×D412yes—
237C4⋊C4×C41C2×D412yes—
238C4⋊C4×C41#4112yes—
239C22⋊C4×C41—24no—
240C22⋊C4×C41—24no—
241C22⋊C4×C41—24no—
242C22⋊C4×C41—22no—
243C22⋊C4×C41—24no—
244C22⋊C4×C41—22no—
245C22⋊C4×C41—42no—
246C22⋊C4×C41—42no—
247C22⋊C4×C41—42no—
248C22⋊C4×C41—42no—
249C22⋊C4×C41—81no—
250C22⋊C4×C41—81no—
251C42×C41—24no—
252C42×C41—21no—
253C42×C41—21no—
254C42×C41—42no—
255C23×C41—21no—
256C23×C41—21no—
257C23×C41—21no—
258C23×C41—21no—
259C23×C41—21no—
260C23×C41—21no—
261C23×C41—21no—
262C23×C41—22no—
263C23×C41—21no—
264C23×C41—21no—
265C23×C41—21no—
266C23×C41—21no—
267C23×C41—21no—
268C23×C41—21no—
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#12012yes—
283C23×C41C22×D411yescharacteristic
284D4×C41—22no—
285D4×C41—22no—
286D4×C41—44no—
287D4×C41—48no—
288D4×C41—41no—
289D4×C41—41no—
290D4×C41—41no—
291D4×C41—41no—
292D4×C41—41no—
293D4×C41—41no—
294D4×C41—84no—
295D4×C41—84no—
296D4×C41—84no—
297C2×C4×C41—21no—
298C2×C4×C41—21no—
299C2×C4×C41—22no—
300C2×C4×C41—22no—
301C2×C4×C41—22no—
302C2×C4×C41—22no—
303C2×C4×C41—21no—
304C2×C4×C41—21no—
305C2×C4×C41—22no—
306C2×C4×C41—21no—
307C2×C4×C41—22no—
308C2×C4×C41—22no—
309C2×C4×C41—22no—
310C2×C4×C41—21no—
311C2×C4×C41—21no—
312C2×C4×C41—21no—
313C2×C4×C41—21no—
314C2×C4×C41—21no—
315C2×C4×C41—21no—
316C2×C4×C41—41no—
317C2×C4×C41—41no—
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#12012yes—
337C2×C4×C41C22×D411yescharacteristic
338C2×C4×C41C22×D411yescharacteristic
339C2×C4×C41C2×#4111yescharacteristic
340C2×C4×C41C2×#4111yescharacteristic
341C2×C4×C41H(5,𝔽2)11yescharacteristic
342C2×C4×C412−1+411yescharacteristic
343C8×C41—22no—
344C8×C41—41no—
345C8×C41—41no—
346C8×C41—41no—
347#25553C4111yesmaximal, characteristic, direct product factor, Sylow
348C22×C41—22no—
349C22×C41—22no—
350C22×C41—22no—
351C22×C41—41no—
352C22×C41—41no—
353C22×C41—41no—
354C22×C41—41no—
355C22×C41—41no—
356C22×C41—41no—
357C22×C41—41no—
358C22×C41—42no—
359C22×C41—41no—
360C22×C41—42no—
361C22×C41—42no—
362C22×C41—41no—
363C22×C41—41no—
364C22×C41—41no—
365C22×C41—81no—
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×C41C2×#12011yescharacteristic
377C22×C41#54611yescharacteristic
378C22×C41#54711yescharacteristic
379C22×C41#57511yescharacteristic
380C22×C41#57511yescharacteristic
381C22×C41#57611yescharacteristic
382C22×C41#57611yescharacteristic
383C4×C41—22no—
384C4×C41—41no—
385C4×C41—41no—
386C4×C41—42no—
387C4×C41—41no—
388C4×C41—42no—
389C4×C41—42no—
390C4×C41—42no—
391C4×C41—81no—
392C4×C41—81no—
393C4×C41#53211yescharacteristic
394C4×C41#53711yescharacteristic
395C4×C41#54611yescharacteristic
396C4×C41#54711yescharacteristic
397C2×#553C2×C4111yescharacteristic, complemented
398C2×#480C2×C4111yescharacteristic, complemented
399C2×#469C2×C4111yescharacteristic, complemented
400#2414C2×C4111yescharacteristic, complemented
401#2059C2×C4111yescharacteristic, complemented
402#2033C2×C4111yescharacteristic, complemented
403#2025C2×C4111yescharacteristic, complemented
404#1999C2×C4111yescharacteristic, complemented
405#1879C2×C4111yescharacteristic, complemented
406#1875C2×C4111yescharacteristic, complemented
407#1875C2×C4111yescharacteristic, complemented
408#1870C2×C4111yescharacteristic, complemented
409#1862C2×C4111yescharacteristic, complemented
410#1854C2×C4111yescharacteristic, complemented
411#1736C2×C4111yescharacteristic, complemented
412C2×C41—42no—
413C2×C41—81no—
414C2×C41—82no—
415C2×C41—161no—
416C2×C41#243011yescharacteristic
417C2×C41#300511yescharacteristic
418C2×C41#300811yescharacteristic
419C2×C41#330911yescharacteristic
420C2×C41#332211yescharacteristic
421C2×C41#334711yescharacteristic
422C2×C41#335511yescharacteristic
423C22×D8C22×C4111yescharacteristic
424C22×M16C22×C4111yescharacteristic
425#553—24no—
426#553—24no—
427C2×#126—21no—
428C2×#125C22×C4111yescharacteristic
429C2×#123—21no—
430C2×#121—21no—
431C2×#121C22×C4111yescharacteristic
432C2×#121C22×C4111yescharacteristic
433C2×#121C22×C4111yescharacteristic
434C2×#121C22×C4111yescharacteristic
435C2×C4×D4—21no—
436C2×C4×D4C22×C4111yescharacteristic
437C2×C4×D4C22×C4111yescharacteristic
438C2×#117C22×C4111yescharacteristic
439C2×#117C22×C4111yescharacteristic
440C22×C4⋊C4C22×C4111yescharacteristic
441#480—24no—
442#469—24no—
443C2×#107C22×C4111yescharacteristic
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×C22⋊C8C22×C4111yescharacteristic
453C2×C22⋊C8C22×C4111yescharacteristic
454C2×C22⋊C8C22×C4111yescharacteristic
455#394—21no—
456#392—21no—
457#390—21no—
458#390C22×C4111yescharacteristic
459#389C22×C4111yescharacteristic
460#388—21no—
461#380C22×C4111yescharacteristic
462#340C22×C4111yescharacteristic
463#340C22×C4111yescharacteristic
464#340C22×C4111yescharacteristic
465#340C22×C4111yescharacteristic
466#340C22×C4111yescharacteristic
467#340C22×C4111yescharacteristic
468#336C22×C4111yescharacteristic
469#336C22×C4111yescharacteristic
470C41#2555311yescharacteristic, direct product factor, Sylow
471C22×D4—21no—
472C22×D4—21no—
473C22×D4—21no—
474C22×D4—21no—
475C22×D4D4×C4111yescharacteristic
476C22×D4C23×C4111yescharacteristic
477C22×D4C23×C4111yescharacteristic
478C23×C4—21no—
479C23×C4—21no—
480C23×C4C23×C4111yescharacteristic
481C23×C4C23×C4111yescharacteristic
482C2×D8—22no—
483C2×D8—22no—
484C2×D8—41no—
485C2×M16—22no—
486C2×M16—22no—
487C2×M16—41no—
488C22×C8C23×C4111yescharacteristic
489C22×C8C23×C4111yescharacteristic
490C22×C8C23×C4111yescharacteristic
491C22×C8C23×C4111yescharacteristic
492#126—28no—
493#125—22no—
494#125—22no—
495#123—28no—
496#121—28no—
497#121—22no—
498#121—22no—
499#121—22no—
500#121—22no—
501#121—22no—
502#121—22no—
503#121—41no—
504#121D4×C4114yescomplemented
505C4×D4—28no—
506C4×D4—22no—
507C4×D4—22no—
508C4×D4—22no—
509C4×D4—22no—
510#117—22no—
511#117—22no—
512#117—22no—
513#117—41no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—22no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4D4×C4111yescharacteristic
520C2×C4⋊C4D4×C4114yescomplemented
521C2×C4⋊C4C23×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⋊C4—21no—
537C2×C22⋊C4D4×C4111yescharacteristic
538C2×C22⋊C4D4×C4111yescharacteristic
539C2×C42—21no—
540C2×C42—21no—
541C2×C42C23×C4111yescharacteristic
542#107—22no—
543#107—22no—
544#106—22no—
545#102—22no—
546#102—22no—
547#102—22no—
548#102—22no—
549#102—22no—
550#102—41no—
551C22⋊C8—22no—
552C22⋊C8—22no—
553C22⋊C8—41no—
554#95—21no—
555#95—21no—
556C24—21no—
557C24—21no—
558C24C2×D4×C4111yescharacteristic
559C24C2×D4×C4111yescharacteristic
560C2×D4—22no—
561C2×D4—24no—
562C2×D4—24no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—41no—
575C2×D4—41no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—42no—
579C2×D4—42no—
580C2×D4—42no—
581C2×D4—81no—
582C2×D4—81no—
583C2×D4—81no—
584C2×D4—81no—
585C2×D4—81no—
586C2×D4C2×D4×C4112yes—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—24no—
596C22×C4—24no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—81no—
606C22×C4—81no—
607C22×C4—81no—
608C22×C4—81no—
609C22×C4C2×D4×C4111yescharacteristic
610C22×C4C2×D4×C4111yescharacteristic
611C22×C4C2×D4×C4111yescharacteristic
612C22×C4C2×D4×C4111yescharacteristic
613C22×C4C2×D4×C4112yes—
614C22×C4C2×D4×C4112yes—
615C22×C4C24×C4111yescharacteristic
616D8—44no—
617M16—44no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8#41×C4112yes—
630C4⋊C4—24no—
631C4⋊C4—24no—
632C4⋊C4—24no—
633C4⋊C4—22no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—81no—
643C4⋊C4C2×D4×C4112yes—
644C4⋊C4C2×D4×C4112yes—
645C4⋊C4C2×D4×C4112yes—
646C4⋊C4#41×C4112yes—
647C22⋊C4—24no—
648C22⋊C4—24no—
649C22⋊C4—24no—
650C22⋊C4—22no—
651C22⋊C4—24no—
652C22⋊C4—22no—
653C22⋊C4—42no—
654C22⋊C4—42no—
655C22⋊C4—42no—
656C22⋊C4—42no—
657C22⋊C4—81no—
658C22⋊C4—81no—
659C42—24no—
660C42—21no—
661C42—21no—
662C42—42no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—22no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
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#120×C4112yes—
691C23C22×D4×C4111yescharacteristic
692D4—22no—
693D4—22no—
694D4—44no—
695D4—48no—
696D4—41no—
697D4—41no—
698D4—41no—
699D4—41no—
700D4—41no—
701D4—41no—
702D4—84no—
703D4—84no—
704D4—84no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—22no—
714C2×C4—21no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
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—84no—
743C2×C4—84no—
744C2×C4#120×C4112yes—
745C2×C4C22×D4×C4111yescharacteristic
746C2×C4C22×D4×C4111yescharacteristic
747C2×C4C2×#41×C4111yescharacteristic
748C2×C4C2×#41×C4111yescharacteristic
749C2×C4H(5,𝔽2)×C4111yescharacteristic
750C2×C42−1+4×C4111yescharacteristic
751C8—22no—
752C8—41no—
753C8—41no—
754C8—41no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—42no—
768C22—41no—
769C22—42no—
770C22—42no—
771C22—41no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22C2×#120×C4111yescharacteristic
784C22C41×#54611yescharacteristic
785C22C41×#54711yescharacteristic
786C22C41×#57511yescharacteristic
787C22C41×#57511yescharacteristic
788C22C41×#57611yescharacteristic
789C22C41×#57611yescharacteristic
790C4—22no—
791C4—42no—
792C4—41no—
793C4—41no—
794C4—42no—
795C4—41no—
796C4—42no—
797C4—42no—
798C4—81no—
799C4—81no—
800C4C41×#53211yescharacteristic
801C4C41×#53711yescharacteristic
802C4C41×#54611yescharacteristic
803C4C41×#54711yescharacteristic
804C2—42no—
805C2—81no—
806C2—82no—
807C2—161no—
808C2C41×#243011yescharacteristic
809C2C41×#300511yescharacteristic
810C2C41×#300811yescharacteristic
811C2C41×#330911yescharacteristic
812C2C41×#332211yescharacteristic
813C2C41×#334711yescharacteristic
814C2C41×#335511yescharacteristic
subgroupG/H
center, socleC23×C41C22×D4
commutator, Frattini, cosocleC22×C4C24×C41
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C41 ◁ C2×C4×D4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C41×#553C2semidirect
2. C2×C41×#480C2semidirect
3. C2×C41×#469C2semidirect
4. C41×#2414C2semidirect
5. C41×#2059C2semidirect
6. C41×#2033C2semidirect
7. C41×#2025C2semidirect
8. C41×#1999C2semidirect
9. C41×#1879C2semidirect
10. C41×#1875C2semidirect
11. C41×#1875C2semidirect
12. C41×#1870C2semidirect
13. C41×#1862C2semidirect
14. C41×#1854C2semidirect
15. C41×#1736C2semidirect
96. #121×C41D4semidirect
112. C2×C4⋊C4×C41D4semidirect
347. #25553C41direct (N × H)
397. C2×#553C2×C41semidirect
398. C2×#480C2×C41semidirect
399. C2×#469C2×C41semidirect
400. #2414C2×C41semidirect
401. #2059C2×C41semidirect
402. #2033C2×C41semidirect
403. #2025C2×C41semidirect
404. #1999C2×C41semidirect
405. #1879C2×C41semidirect
406. #1875C2×C41semidirect
407. #1875C2×C41semidirect
408. #1870C2×C41semidirect
409. #1862C2×C41semidirect
410. #1854C2×C41semidirect
411. #1736C2×C41semidirect
470. C41#25553direct (N × H)
504. #121D4×C41semidirect
520. C2×C4⋊C4D4×C41semidirect

Maximal subgroups

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

subgroupindex
C2×C41×#5532
C2×C41×#4802
C2×C41×#4692
C41×#24142
C41×#20592
C41×#20332
C41×#20252
C41×#19992
C41×#18792
C41×#18752
C41×#18702
C41×#18622
C41×#18542
C41×#17362
#2555341