Finite Group Databasebeta

← #30548402

Subgroups — #30548402

Order 15616.

2570 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459115C211yesmaximal, characteristic, complemented
2C22×C4×D244C211yesmaximal, characteristic, complemented
3#21455959C214yesmaximal, complemented
4#21455919C212yesmaximal, complemented
5#21455911C212yesmaximal, complemented
6#21455868C214yesmaximal, complemented
7#21455828C212yesmaximal, complemented
8#21455820C212yesmaximal, complemented
9#21455744C212yesmaximal, complemented
10#21455618C212yesmaximal, complemented
11#21455285C212yesmaximal, complemented
12#21455049C212yesmaximal, complemented
13C4×#14519805C214yesmaximal, complemented
14C61×#2920C211yesmaximal, characteristic, complemented
15C23×D244C2211yescharacteristic
16C23×C4×D61—21no—
17C2×#14519805C2214yes—
18#16840319C2211yescharacteristic, complemented
19#16840319C2211yescharacteristic, complemented
20#16840319C2211yescharacteristic, complemented
21#16840312C2211yescharacteristic, complemented
22#16840312C2211yescharacteristic, complemented
23#16840312C2211yescharacteristic, complemented
24#16840296—21no—
25#16840296—21no—
26#16840296—21no—
27#16840296—21no—
28#16840296C2212yescomplemented
29#16840296C2212yescomplemented
30#16840273—21no—
31#16840273—21no—
32#16840273C2212yes—
33C4×#11758222—21no—
34C4×#11758222—21no—
35C4×#11758222C2212yescomplemented
36C2×C4×D244—21no—
37C2×C4×D244—21no—
38C2×C4×D244—21no—
39C2×C4×D244—21no—
40C2×C4×D244—21no—
41C2×C4×D244—21no—
42C2×C4×D244C2212yes—
43C2×C4×D244C2212yes—
44C2×C4×D244C2212yes—
45C2×C4×D244C2212yes—
46C2×C4×D244C2212yes—
47C2×C4×D244C2212yes—
48C22×C4⋊Dic61C2211yescharacteristic
49C22×#11758198—21no—
50#16840098C2214yescomplemented
51#16840093C2214yescomplemented
52#16840081C2214yescomplemented
53#16840076C2214yescomplemented
54#16840063C2218yescomplemented
55#16840053C2214yescomplemented
56#16840043C2214yescomplemented
57#16839978C2218yescomplemented
58#16839968C2214yescomplemented
59#16839958C2214yescomplemented
60#16839915C2214yes—
61#16839915C2214yes—
62#16839898C2214yes—
63#16839898C2214yes—
64#16839875C2218yescomplemented
65#16839864C2218yescomplemented
66C4×#11758190C2218yescomplemented
67C4×D488C2218yescomplemented
68#16839804C2214yescomplemented
69#16839768C2214yes—
70#16839764C2214yescomplemented
71C22×C42×C61C2211yescharacteristic
72C61×#432C2212yescomplemented
73C61×#432C2212yescomplemented
74C61×#431C2212yescomplemented
75C61×#431C2212yescomplemented
76C61×#423C2212yescomplemented
77C61×#407C2212yes—
78C4×M16×C61C2212yescomplemented
79C24×D61—21no—
80C2×#11758222—21no—
81C2×#11758222—21no—
82C2×#11758222C2312yes—
83C22×D244—21no—
84C22×D244—21no—
85C22×D244—21no—
86C22×D244—28no—
87C22×D244C2312yes—
88C22×D244C2312yes—
89C22×D244C2312yes—
90C23×Dic61—21no—
91C22×C4×D61—22no—
92C22×C4×D61—22no—
93C22×C4×D61—22no—
94C22×C4×D61—22no—
95C22×C4×D61—22no—
96C22×C4×D61—22no—
97C22×C4×D61—48no—
98#14519805—216no—
99C2×#11758190C2318yes—
100C2×D488C2318yes—
101#14519777C2311yescharacteristic, complemented
102#14519777C2311yescharacteristic, complemented
103#14519777C2311yescharacteristic, complemented
104#14519774C2311yescharacteristic, complemented
105#14519771—22no—
106#14519771—22no—
107#14519769—21no—
108#14519769—21no—
109#14519769C2312yescomplemented
110#14519765—21no—
111#14519765—21no—
112#14519765C2312yescomplemented
113#14519760—22no—
114#14519760—22no—
115#14519760—22no—
116#14519756—21no—
117#14519756—21no—
118#14519756—21no—
119#14519756—21no—
120#14519756C2312yes—
121#14519756C2312yes—
122#14519751—21no—
123#14519751—21no—
124#14519751—21no—
125#14519751—21no—
126#14519751C2312yes—
127#14519751C2312yes—
128#14519746—22no—
129C4×Dic122—21no—
130C4×Dic122—21no—
131C4×Dic122—21no—
132C4×Dic122—21no—
133C4×Dic122C2312yescomplemented
134C4×Dic122C2312yescomplemented
135C4×D244—22no—
136C4×D244—22no—
137C4×D244—22no—
138C4×D244—22no—
139C4×D244—22no—
140C4×D244—22no—
141C4×D244—22no—
142C4×D244—22no—
143C4×D244—22no—
144C4×D244—22no—
145C4×D244—22no—
146C4×D244—22no—
147C4×D244—21no—
148C4×D244—21no—
149C4×D244—21no—
150C4×D244—21no—
151C4×D244C2314yes—
152C4×D244C2314yes—
153C4×D244C2314yes—
154C4×D244C2314yes—
155C4×D244C2312yescomplemented
156C4×D244C2312yescomplemented
157C4×C22⋊D61—22no—
158C4×C22⋊D61—22no—
159C4×C22⋊D61—22no—
160C4×C22⋊D61—22no—
161C4×C22⋊D61—22no—
162C4×C22⋊D61—22no—
163#14519736—21no—
164#14519736—21no—
165#14519736C2312yes—
166#14519734—22no—
167#14519734—22no—
168#14519734—22no—
169C2×C4⋊Dic61—21no—
170C2×C4⋊Dic61—21no—
171C2×C4⋊Dic61—21no—
172C2×C4⋊Dic61C2312yes—
173C2×C4⋊Dic61C2312yes—
174C2×C4⋊Dic61C2312yes—
175C2×#11758198—22no—
176C2×#11758198—22no—
177C2×#11758198—22no—
178C2×#11758198—22no—
179C2×#11758198—22no—
180C2×#11758198—22no—
181C42×D61—22no—
182#14519711C2318yescomplemented
183#14519709C2318yescomplemented
184#14519702C2318yescomplemented
185#14519699C2318yes—
186#14519699C2318yes—
187#14519699C2318yescomplemented
188C23×C4×C61D411yescharacteristic
189C23×C4×C61D411yescharacteristic
190C23×C4×C61C2311yescharacteristic
191C2×M16×C61C2314yes—
192C2×C42×C61D411yescharacteristic
193C2×C42×C61D411yescharacteristic
194C2×C42×C61D411yescharacteristic
195C2×C42×C61D411yescharacteristic
196C2×C42×C61D411yescharacteristic
197C2×C42×C61D411yescharacteristic
198C2×C42×C61C2311yescharacteristic
199C2×C42×C61C2311yescharacteristic
200C2×C42×C61C2311yescharacteristic
201C2×C42×C61C2311yescharacteristic
202C2×C42×C61C2311yescharacteristic
203C2×C42×C61C2311yescharacteristic
204C4⋊C8×C61C2314yescomplemented
205C4⋊C8×C61C2314yescomplemented
206C22⋊C8×C61C2314yes—
207C22⋊C8×C61C2314yes—
208#97×C61C2314yescomplemented
209C4×C8×C61C2314yescomplemented
210C24×C61C2×D411yescharacteristic
211C23×D61—28no—
212C23×D61—22no—
213C23×D61—22no—
214C23×D61—22no—
215C23×D61—44no—
216C23×D61—44no—
217C22×C4×C61—24no—
218C22×C4×C61—24no—
219C22×C4×C61—42no—
220C22×C4×C61C2×D411yescharacteristic
221C22×C4×C61C2×D411yescharacteristic
222C22×C4×C61C2×D411yescharacteristic
223C22×C4×C61C2×D411yescharacteristic
224C22×C4×C61C2×D411yescharacteristic
225C22×C4×C61C2×D411yescharacteristic
226C22×C4×C61C2×D411yescharacteristic
227C22×C4×C61C2×D411yescharacteristic
228C22×C4×C61C2×D411yescharacteristic
229C22×C4×C61C2×D411yescharacteristic
230C22×C4×C61C2×D411yescharacteristic
231C22×C4×C61C2×D411yescharacteristic
232C22×C4×C61C2×D411yescharacteristic
233C22×C4×C61C2×D411yescharacteristic
234C22×C4×C61C2×D411yescharacteristic
235C22×C4×C61C2411yescharacteristic
236C22×C4×C61C2411yescharacteristic
237C22×C4×C61C2411yescharacteristic
238C2×C22⋊D61—22no—
239C2×C22⋊D61—22no—
240C2×C22⋊D61—22no—
241C22×Dic61—22no—
242C22×Dic61—22no—
243C22×Dic61—22no—
244C22×Dic61—44no—
245#11758222—28no—
246#11758222—44no—
247#11758222—44no—
248C2×D244—28no—
249C2×D244—28no—
250C2×D244—28no—
251C2×D244—22no—
252C2×D244—22no—
253C2×D244—22no—
254C2×D244—24no—
255C2×D244—28no—
256C2×D244—28no—
257C2×D244—21no—
258C2×D244—21no—
259C2×D244#4118yescomplemented
260C2×D244C2412yes—
261C2×D244C2414yes—
262C2×C4×D61—24no—
263C2×C4×D61—24no—
264C2×C4×D61—24no—
265C2×C4×D61—24no—
266C2×C4×D61—22no—
267C2×C4×D61—22no—
268C2×C4×D61—22no—
269C2×C4×D61—48no—
270C2×C4×D61—48no—
271C2×C4×D61—48no—
272C2×C4×D61—48no—
273C2×C4×D61—48no—
274C2×C4×D61—48no—
275C2×Dic122—21no—
276C2×Dic122—21no—
277C2×Dic122C2412yes—
278M16×C61—28no—
279C2×C8×C61C2418yes—
280C42×C61C2×D411yescharacteristic
281C42×C61C2×D411yescharacteristic
282C42×C61C2×D411yescharacteristic
283C42×C61C2×D411yescharacteristic
284C42×C61C2×D411yescharacteristic
285C42×C61C2×D411yescharacteristic
286C42×C61C2×D411yescharacteristic
287C42×C61C2×D411yescharacteristic
288C42×C61C2×D411yescharacteristic
289C42×C61C2×D411yescharacteristic
290C42×C61C2×D411yescharacteristic
291C42×C61C2×D411yescharacteristic
292C42×C61C2411yescharacteristic
293C42×C61C2411yescharacteristic
294C42×C61C2411yescharacteristic
295C42×C61C2411yescharacteristic
296C22⋊Dic61—22no—
297C22⋊Dic61—22no—
298C22⋊Dic61—22no—
299#11758198—24no—
300#11758198—24no—
301#11758198—24no—
302#11758198—24no—
303#11758198—22no—
304#11758198—22no—
305#11758198—22no—
306#11758198—22no—
307#11758198—22no—
308#11758198—22no—
309C4⋊Dic61—22no—
310C4⋊Dic61—22no—
311C4⋊Dic61—22no—
312C4⋊Dic61—21no—
313C4⋊Dic61—21no—
314C4⋊Dic61—21no—
315C4⋊Dic61—21no—
316C4⋊Dic61C2412yes—
317C4⋊Dic61C2412yes—
318C4⋊Dic61C2414yes—
319#11758196—22no—
320#11758196—22no—
321#11758196—22no—
322#11758196—22no—
323#11758196—22no—
324#11758196—22no—
325C4×Dic61—22no—
326C4×Dic61—22no—
327C4×Dic61—22no—
328D488—216no—
329#11758190—216no—
330C23×C61—22no—
331C23×C61—22no—
332C23×C61—22no—
333C23×C61C22×D411yescharacteristic
334C23×C61C22×D411yescharacteristic
335C23×C61C22×D411yescharacteristic
336C22×D61—28no—
337C22×D61—28no—
338C22×D61—28no—
339C22×D61—24no—
340C22×D61—22no—
341C22×D61—44no—
342C22×D61—44no—
343C22×D61—432no—
344C22×D61—44no—
345C22×D61—44no—
346C22×D61—44no—
347C22×D61—44no—
348C2×C4×C61—22no—
349C2×C4×C61—22no—
350C2×C4×C61—22no—
351C2×C4×C61—22no—
352C2×C4×C61—22no—
353C2×C4×C61—22no—
354C2×C4×C61—22no—
355C2×C4×C61—22no—
356C2×C4×C61—22no—
357C2×C4×C61—22no—
358C2×C4×C61—22no—
359C2×C4×C61—22no—
360C2×C4×C61—41no—
361C2×C4×C61—41no—
362C2×C4×C61—41no—
363C2×C4×C61—41no—
364C2×C4×C61AGL(1,ℤ/8)14yescomplemented
365C2×C4×C61C22×D411yescharacteristic
366C2×C4×C61C22×D411yescharacteristic
367C2×C4×C61C22×D411yescharacteristic
368C2×C4×C61C22×D411yescharacteristic
369C2×C4×C61C22×D411yescharacteristic
370C2×C4×C61C22×D411yescharacteristic
371C2×C4×C61C22×D411yescharacteristic
372C2×C4×C61C22×D411yescharacteristic
373C2×C4×C61C22×D411yescharacteristic
374C2×C4×C61C22×D411yescharacteristic
375C2×C4×C61C22×D411yescharacteristic
376C2×C4×C61C2×#4114yes—
377C2×C4×C61C2511yescharacteristic
378C22⋊D61—44no—
379C22⋊D61—44no—
380C22⋊D61—44no—
381C2×Dic61—22no—
382C2×Dic61—22no—
383C2×Dic61—22no—
384C2×Dic61—24no—
385C2×Dic61—44no—
386C2×Dic61—44no—
387C2×Dic61—44no—
388D244—28no—
389D244—28no—
390D244—28no—
391D244—24no—
392D244—24no—
393D244—42no—
394D244—42no—
395D244C2×#4118yes—
396C4×D61—48no—
397C4×D61—48no—
398C4×D61—44no—
399C4×D61—44no—
400C4×D61—48no—
401C4×D61—48no—
402C4×D61—44no—
403Dic122—24no—
404Dic122—42no—
405Dic122—42no—
406C8×C61—28no—
407#60558—611nomaximal, Sylow
408C22×C61—28no—
409C22×C61—21no—
410C22×C61—21no—
411C22×C61—21no—
412C22×C61—21no—
413C22×C61—21no—
414C22×C61—21no—
415C22×C61#52512yes—
416C22×C61C2×AGL(1,ℤ/8)12yes—
417C22×C61#57512yes—
418C22×C61C23×D411yescharacteristic
419C2×D61—28no—
420C2×D61—416no—
421C2×D61—416no—
422C2×D61—416no—
423C2×D61—44no—
424C2×D61—44no—
425C2×D61—42no—
426C2×D61—42no—
427C2×D61—42no—
428C4×C61—21no—
429C4×C61—21no—
430C4×C61—21no—
431C4×C61—21no—
432C4×C61—21no—
433C4×C61—21no—
434C4×C61—21no—
435C4×C61—21no—
436C4×C61#52512yes—
437C4×C61C2×AGL(1,ℤ/8)12yes—
438C4×C61C2×AGL(1,ℤ/8)12yes—
439C4×C61C22×#4112yes—
440Dic61—42no—
441Dic61—42no—
442Dic61—44no—
443Dic61—42no—
444#3444—611no—
445C22×C4×D4—611no—
446#3114—614no—
447#3110—612no—
448#3109—612no—
449#3105—614no—
450#3101—612no—
451#3100—612no—
452#3092—612no—
453#3077—612no—
454#3036—612no—
455#3003—612no—
456C4×AGL(1,ℤ/8)—614no—
457#2920D6111yescharacteristic, complemented
458C2×C61—22no—
459C2×C61—22no—
460C2×C61—22no—
461C2×C61C2×#52511yescharacteristic
462C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
463C2×C61C2×#57511yescharacteristic
464D61—48no—
465D61—82no—
466C23×D4—611no—
467C24×C4—1221no—
468C2×AGL(1,ℤ/8)—614no—
469#533—611no—
470#533—611no—
471#533—611no—
472#532—611no—
473#532—611no—
474#532—611no—
475#529—612no—
476#529—612no—
477#529—1221no—
478#529—1221no—
479#529—1221no—
480#529—1221no—
481#525—612no—
482#525—1221no—
483#525—1221no—
484C4×#41—612no—
485C4×#41—1221no—
486C4×#41—1221no—
487C2×C4×D4—612no—
488C2×C4×D4—612no—
489C2×C4×D4—612no—
490C2×C4×D4—612no—
491C2×C4×D4—612no—
492C2×C4×D4—612no—
493C2×C4×D4—1221no—
494C2×C4×D4—1221no—
495C2×C4×D4—1221no—
496C2×C4×D4—1221no—
497C2×C4×D4—1221no—
498C2×C4×D4—1221no—
499C22×C4⋊C4—611no—
500C22×C22⋊C4—1221no—
501C22×C42C2×D6111yescharacteristic
502#484—614no—
503#483—614no—
504#481—614no—
505#480—614no—
506#478—618no—
507#476—614no—
508#474—614no—
509#463—618no—
510#461—614no—
511#459—614no—
512#450—614no—
513#450—614no—
514#447—614no—
515#447—614no—
516#442—618no—
517#440—618no—
518C4×SD16—618no—
519C4×D8—618no—
520#432C2×D6112yescomplemented
521#432C2×D6112yescomplemented
522#431C2×D6112yescomplemented
523#431C2×D6112yescomplemented
524#428—614no—
525#423C2×D6112yescomplemented
526#418—614no—
527#417—614no—
528#407C2×D6112yes—
529C4×M16C2×D6112yescomplemented
530C61#6055811yescharacteristic, complemented, Sylow
531C25—1221no—
532C2×#41—612no—
533C2×#41—1221no—
534C2×#41—1221no—
535C22×D4—612no—
536C22×D4—612no—
537C22×D4—612no—
538C22×D4—1228no—
539C22×D4—1221no—
540C22×D4—1221no—
541C22×D4—1221no—
542C23×C4—1221no—
543C23×C4—1222no—
544C23×C4—1222no—
545C23×C4—1222no—
546C23×C4—1222no—
547C23×C4—1222no—
548C23×C4—1222no—
549C23×C4—2448no—
550C23×C4D24411yescharacteristic
551C23×C4D24411yescharacteristic
552C23×C4C22×D6111yescharacteristic
553AGL(1,ℤ/8)—12216no—
554C2×SD16—618no—
555C2×D8—618no—
556C2×M16C22×D6114yes—
557C4⋊Q8—611no—
558C4⋊Q8—611no—
559C4⋊Q8—611no—
560#127—611no—
561#126—1222no—
562#126—1222no—
563#125—612no—
564#125—1221no—
565#125—1221no—
566#124—612no—
567#124—1221no—
568#124—1221no—
569#123—1222no—
570#123—1222no—
571#123—1222no—
572C22⋊Q8—612no—
573C22⋊Q8—612no—
574C22⋊Q8—1221no—
575C22⋊Q8—1221no—
576C22⋊Q8—1221no—
577C22⋊Q8—1221no—
578#121—612no—
579#121—612no—
580#121—1221no—
581#121—1221no—
582#121—1221no—
583#121—1221no—
584#120—1222no—
585C4×Q8—612no—
586C4×Q8—612no—
587C4×Q8—1221no—
588C4×Q8—1221no—
589C4×Q8—1221no—
590C4×Q8—1221no—
591C4×D4—614no—
592C4×D4—614no—
593C4×D4—614no—
594C4×D4—614no—
595C4×D4—612no—
596C4×D4—612no—
597C4×D4—1222no—
598C4×D4—1222no—
599C4×D4—1222no—
600C4×D4—1222no—
601C4×D4—1222no—
602C4×D4—1222no—
603C4×D4—1222no—
604C4×D4—1222no—
605C4×D4—1222no—
606C4×D4—1222no—
607C4×D4—1222no—
608C4×D4—1222no—
609C4×D4—1222no—
610C4×D4—1222no—
611C4×D4—1222no—
612C4×D4—1222no—
613C4×D4—1222no—
614C4×D4—1222no—
615C4×D4—1221no—
616C4×D4—1221no—
617C4×D4—1221no—
618C4×D4—1221no—
619#117—612no—
620#117—1221no—
621#117—1221no—
622#117—1222no—
623#117—1222no—
624#117—1222no—
625C2×C4⋊C4—612no—
626C2×C4⋊C4—612no—
627C2×C4⋊C4—612no—
628C2×C4⋊C4—1221no—
629C2×C4⋊C4—1221no—
630C2×C4⋊C4—1221no—
631C2×C22⋊C4—1222no—
632C2×C22⋊C4—1222no—
633C2×C22⋊C4—1222no—
634C2×C22⋊C4—1222no—
635C2×C22⋊C4—1222no—
636C2×C22⋊C4—1222no—
637C2×C42—1222no—
638C2×C42D24411yescharacteristic
639C2×C42D24411yescharacteristic
640C2×C42D24411yescharacteristic
641C2×C42D24411yescharacteristic
642C2×C42D24411yescharacteristic
643C2×C42D24411yescharacteristic
644C2×C42C22×D6111yescharacteristic
645C2×C42C22×D6111yescharacteristic
646C2×C42C22×D6111yescharacteristic
647C2×C42C22×D6111yescharacteristic
648C2×C42C22×D6111yescharacteristic
649C2×C42C22×D6111yescharacteristic
650#107—618no—
651#106—618no—
652C4⋊C8C22×D6114yescomplemented
653C4⋊C8C22×D6114yescomplemented
654#103—618no—
655#102—618no—
656#102—618no—
657#102—618no—
658C22⋊C8C22×D6114yes—
659C22⋊C8C22×D6114yes—
660#97C22×D6114yescomplemented
661C4×C8C22×D6114yescomplemented
662C24—1228no—
663C24—1222no—
664C24—1222no—
665C24—1222no—
666C24—2444no—
667C24—2444no—
668C24C2×D24411yescharacteristic
669#41—1228no—
670#41—2444no—
671#41—2444no—
672C2×Q8—612no—
673C2×Q8—1221no—
674C2×Q8—1221no—
675C2×D4—618no—
676C2×D4—614no—
677C2×D4—612no—
678C2×D4—1228no—
679C2×D4—1228no—
680C2×D4—1228no—
681C2×D4—1228no—
682C2×D4—1228no—
683C2×D4—1222no—
684C2×D4—1222no—
685C2×D4—1222no—
686C2×D4—1222no—
687C2×D4—1222no—
688C2×D4—1222no—
689C2×D4—1221no—
690C2×D4—1221no—
691C2×D4—1224no—
692C22×C4—24no—
693C22×C4—24no—
694C22×C4—42no—
695C22×C4—1222no—
696C22×C4—1222no—
697C22×C4—1222no—
698C22×C4—1222no—
699C22×C4—1222no—
700C22×C4—1224no—
701C22×C4—1224no—
702C22×C4—1224no—
703C22×C4—1222no—
704C22×C4—1224no—
705C22×C4—2448no—
706C22×C4—2448no—
707C22×C4—2448no—
708C22×C4—2448no—
709C22×C4—2448no—
710C22×C4—2444no—
711C22×C4—2448no—
712C22×C4C2×D24411yescharacteristic
713C22×C4C2×D24411yescharacteristic
714C22×C4C2×D24411yescharacteristic
715C22×C4C2×D24411yescharacteristic
716C22×C4C2×D24411yescharacteristic
717C22×C4C2×D24411yescharacteristic
718C22×C4C2×D24411yescharacteristic
719C22×C4C2×D24411yescharacteristic
720C22×C4C2×D24411yescharacteristic
721C22×C4C2×D24411yescharacteristic
722C22×C4C2×D24411yescharacteristic
723C22×C4C2×D24411yescharacteristic
724C22×C4C2×D24411yescharacteristic
725C22×C4C2×D24411yescharacteristic
726C22×C4C2×D24411yescharacteristic
727C22×C4C23×D6111yescharacteristic
728C22×C4C23×D6111yescharacteristic
729C22×C4C23×D6111yescharacteristic
730SD16—12216no—
731D8—12216no—
732M16—28no—
733C2×C8C23×D6118yes—
734C4⋊C4—612no—
735C4⋊C4—612no—
736C4⋊C4—614no—
737C4⋊C4—1222no—
738C4⋊C4—1222no—
739C4⋊C4—1222no—
740C4⋊C4—1222no—
741C4⋊C4—1222no—
742C4⋊C4—1222no—
743C4⋊C4—1222no—
744C4⋊C4—1222no—
745C4⋊C4—1222no—
746C4⋊C4—1221no—
747C4⋊C4—1221no—
748C4⋊C4—1221no—
749C4⋊C4—1221no—
750C22⋊C4—1222no—
751C22⋊C4—1222no—
752C22⋊C4—1222no—
753C22⋊C4—1224no—
754C22⋊C4—1224no—
755C22⋊C4—1224no—
756C22⋊C4—1224no—
757C22⋊C4—1222no—
758C22⋊C4—1222no—
759C22⋊C4—1222no—
760C22⋊C4—1222no—
761C22⋊C4—1222no—
762C22⋊C4—1222no—
763C42—1222no—
764C42—1222no—
765C42—1222no—
766C42C2×D24411yescharacteristic
767C42C2×D24411yescharacteristic
768C42C2×D24411yescharacteristic
769C42C2×D24411yescharacteristic
770C42C2×D24411yescharacteristic
771C42C2×D24411yescharacteristic
772C42C2×D24411yescharacteristic
773C42C2×D24411yescharacteristic
774C42C2×D24411yescharacteristic
775C42C2×D24411yescharacteristic
776C42C2×D24411yescharacteristic
777C42C2×D24411yescharacteristic
778C42C23×D6111yescharacteristic
779C42C23×D6111yescharacteristic
780C42C23×D6111yescharacteristic
781C42C23×D6111yescharacteristic
782C23—22no—
783C23—22no—
784C23—22no—
785C23—1228no—
786C23—1228no—
787C23—1228no—
788C23—1224no—
789C23—1222no—
790C23—2444no—
791C23—2444no—
792C23—24432no—
793C23—2444no—
794C23—2444no—
795C23—2444no—
796C23—2444no—
797C23C22×D24411yescharacteristic
798C23C22×D24411yescharacteristic
799C23C22×D24411yescharacteristic
800Q8—1224no—
801Q8—2442no—
802Q8—2442no—
803D4—618no—
804D4—1228no—
805D4—1228no—
806D4—1228no—
807D4—1224no—
808D4—1224no—
809D4—2442no—
810D4—2444no—
811D4—2444no—
812D4—2444no—
813D4—2442no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—1222no—
831C2×C4—1222no—
832C2×C4—1222no—
833C2×C4—1224no—
834C2×C4—2448no—
835C2×C4—2448no—
836C2×C4—2444no—
837C2×C4—2444no—
838C2×C4—2444no—
839C2×C4—2444no—
840C2×C4—2444no—
841C2×C4—2448no—
842C2×C4—2448no—
843C2×C4—2444no—
844C2×C4#1451980514yescomplemented
845C2×C4C22×D24411yescharacteristic
846C2×C4C22×D24411yescharacteristic
847C2×C4C22×D24411yescharacteristic
848C2×C4C22×D24411yescharacteristic
849C2×C4C22×D24411yescharacteristic
850C2×C4C22×D24411yescharacteristic
851C2×C4C22×D24411yescharacteristic
852C2×C4C22×D24411yescharacteristic
853C2×C4C22×D24411yescharacteristic
854C2×C4C22×D24411yescharacteristic
855C2×C4C22×D24411yescharacteristic
856C2×C4#41×D6114yes—
857C2×C4C24×D6111yescharacteristic
858C8—28no—
859C22—28no—
860C22—21no—
861C22—21no—
862C22—21no—
863C22—21no—
864C22—21no—
865C22—21no—
866C22—1228no—
867C22—24416no—
868C22—24416no—
869C22—24416no—
870C22—2442no—
871C22—2442no—
872C22—2442no—
873C22—2444no—
874C22—2444no—
875C22#1684027412yes—
876C22C2×#1451980512yes—
877C22#1684056212yes—
878C22C23×D24411yescharacteristic
879C4—21no—
880C4—21no—
881C4—21no—
882C4—21no—
883C4—21no—
884C4—21no—
885C4—21no—
886C4—21no—
887C4—2444no—
888C4—2442no—
889C4—2442no—
890C4—2442no—
891C4#1684027412yes—
892C4C2×#1451980512yes—
893C4C2×#1451980512yes—
894C4C2×#41×D6112yes—
895C2—22no—
896C2—22no—
897C2—22no—
898C2—4882no—
899C2—2448no—
900C2C2×#1684027411yescharacteristic
901C2C22×#1451980511yescharacteristic
902C2C2×#1684056211yescharacteristic
subgroupG/H
centerC2×C4C22×D244
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#2920C2
socleC22×C61C23×D4
hypercenter#2920D61
hypocenterC61#60558
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ #2920

Complements

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

NH ≅ G/Ntype
1. #21459115C2semidirect
2. C22×C4×D244C2semidirect
3. #21455959C2semidirect
4. #21455919C2semidirect
5. #21455911C2semidirect
6. #21455868C2semidirect
7. #21455828C2semidirect
8. #21455820C2semidirect
9. #21455744C2semidirect
10. #21455618C2semidirect
11. #21455285C2semidirect
12. #21455049C2semidirect
13. C4×#14519805C2semidirect
14. C61×#2920C2semidirect
18. #16840319C22semidirect
19. #16840319C22semidirect
20. #16840319C22semidirect
21. #16840312C22semidirect
22. #16840312C22semidirect
23. #16840312C22semidirect
28. #16840296C22semidirect
29. #16840296C22semidirect
35. C4×#11758222C22semidirect
50. #16840098C22semidirect
51. #16840093C22semidirect
52. #16840081C22semidirect
53. #16840076C22semidirect
54. #16840063C22semidirect
55. #16840053C22semidirect
56. #16840043C22semidirect
57. #16839978C22semidirect
58. #16839968C22semidirect
59. #16839958C22semidirect
64. #16839875C22semidirect
65. #16839864C22semidirect
66. C4×#11758190C22semidirect
67. C4×D488C22semidirect
68. #16839804C22semidirect
70. #16839764C22semidirect
72. C61×#432C22semidirect
73. C61×#432C22semidirect
74. C61×#431C22semidirect
75. C61×#431C22semidirect
76. C61×#423C22semidirect
78. C4×M16×C61C22semidirect
101. #14519777C23semidirect
102. #14519777C23semidirect
103. #14519777C23semidirect
104. #14519774C23semidirect
109. #14519769C23semidirect
112. #14519765C23semidirect
133. C4×Dic122C23semidirect
134. C4×Dic122C23semidirect
155. C4×D244C23semidirect
156. C4×D244C23semidirect
182. #14519711C23semidirect
183. #14519709C23semidirect
184. #14519702C23semidirect
187. #14519699C23semidirect
204. C4⋊C8×C61C23semidirect
205. C4⋊C8×C61C23semidirect
208. #97×C61C23semidirect
209. C4×C8×C61C23semidirect
259. C2×D244#41semidirect
364. C2×C4×C61AGL(1,ℤ/8)semidirect
457. #2920D61semidirect
520. #432C2×D61semidirect
521. #432C2×D61semidirect
522. #431C2×D61semidirect
523. #431C2×D61semidirect
525. #423C2×D61semidirect
529. C4×M16C2×D61semidirect
530. C61#60558semidirect
652. C4⋊C8C22×D61semidirect
653. C4⋊C8C22×D61semidirect
660. #97C22×D61semidirect
661. C4×C8C22×D61semidirect
844. C2×C4#14519805semidirect

Maximal subgroups

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

subgroupindex
#214591152
C22×C4×D2442
#214559592
#214559192
#214559112
#214558682
#214558282
#214558202
#214557442
#214556182
#214552852
#214550492
C4×#145198052
C61×#29202
#6055861