Finite Group Databasebeta

← #29685669

Subgroups — #29685669

Order 15616.

1868 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D61C211yesmaximal, characteristic
2C2×#16839914C211yesmaximal, characteristic
3C2×#16839864C211yesmaximal, characteristic, complemented
4C2×#16839862C211yesmaximal, characteristic, complemented
5C4×#14519757C211yesmaximal, characteristic, complemented
6#21446154C211yesmaximal, characteristic, complemented
7#21446151C211yesmaximal, characteristic, complemented
8#21446125C211yesmaximal, characteristic, complemented
9#21446068C211yesmaximal, characteristic, complemented
10#21446067C211yesmaximal, characteristic, complemented
11#21446008C211yesmaximal, characteristic, complemented
12#21445748C211yesmaximal, characteristic
13#21445647C211yesmaximal, characteristic, complemented
14#21445582C211yesmaximal, characteristic, complemented
15C61×#1762C211yesmaximal, characteristic, complemented
16C22×D4×D61C2211yescharacteristic
17C23×C4×D61—21no—
18C22×#11758190C2211yescharacteristic
19C22×#11758200C2211yescharacteristic
20C2×#14519757C2211yescharacteristic
21C2×C4×Dic122C2211yescharacteristic, complemented
22C2×C4×D244C2211yescharacteristic
23C2×D4×Dic61C2211yescharacteristic
24C2×#14519739C2211yescharacteristic
25C2×C4×C22⋊D61—21no—
26C2×#14519737—21no—
27C4×D4×D61—24no—
28C4×D4×D61—24no—
29C2×C4⋊C4×D61C2211yescharacteristic
30C2×C22⋊C4×D61—21no—
31C2×C42×D61C2211yescharacteristic
32#16839914C418yescomplemented
33#16839864—24no—
34#16839862—24no—
35C2×#14519711C2211yescharacteristic, complemented
36C2×#14519710C2211yescharacteristic, complemented
37C2×#14519702C2211yescharacteristic, complemented
38C2×#14519700C2211yescharacteristic, complemented
39C2×#14519699C2211yescharacteristic
40C2×#14519698C2211yescharacteristic
41C2×#14519697C2211yescharacteristic
42C2×#14519697C2211yescharacteristic
43C2×#14519689C2211yescharacteristic
44C2×#14519689C2211yescharacteristic
45C2×#14519688C2211yescharacteristic, complemented
46#16839667C2211yescharacteristic, complemented
47#16839661C2211yescharacteristic, complemented
48#16839647—21no—
49#16839636—21no—
50#16839619C2211yescharacteristic
51C4×C4⋊Dic61—21no—
52C4×#11758198—21no—
53#16839524C2211yescharacteristic, complemented
54#16839524C2211yescharacteristic, complemented
55#16839516C2211yescharacteristic, complemented
56#16839516C2211yescharacteristic, complemented
57C2×C4×D4×C61C2211yescharacteristic
58C2×#102×C61C2211yescharacteristic
59C2×#102×C61C2211yescharacteristic
60C2×#97×C61C2211yescharacteristic, complemented
61C4×C4⋊C4×C61C2211yescharacteristic, complemented
62C61×#340C2211yescharacteristic, complemented
63C61×#340C2211yescharacteristic, complemented
64C24×D61—21no—
65C22×Dic122C2311yescharacteristic
66C22×D244C2311yescharacteristic
67C22×C22⋊D61—21no—
68C2×D4×D61—22no—
69C2×D4×D61—22no—
70C2×D4×D61—22no—
71C2×D4×D61—22no—
72C2×D4×D61—22no—
73C2×D4×D61C2×C414yes—
74C23×Dic61—21no—
75C22×C4×D61—28no—
76C22×C4×D61—21no—
77C22×C4×D61—21no—
78C22×C4×D61—21no—
79C22×C4×D61—44no—
80C22×C4×D61—44no—
81C22×C4×D61D411yescharacteristic
82C22×C4×D61D411yescharacteristic
83C22×C4×D61C2311yescharacteristic
84C2×#11758190—22no—
85C2×#11758190—22no—
86C2×#11758190C2×C414yescomplemented
87C2×#11758200—22no—
88C2×#11758200—22no—
89C2×#11758200C2×C414yescomplemented
90C22×#92418C2311yescharacteristic
91C22×#92418C2311yescharacteristic
92#14519757—22no—
93#14519757C2×C414yescomplemented
94C4×Dic122—22no—
95C4×Dic122—22no—
96C4×D244—22no—
97C4×D244D414yes—
98D4×Dic61—22no—
99D4×Dic61—22no—
100#14519739—22no—
101#14519739—22no—
102C4×C22⋊D61—28no—
103#14519737—28no—
104C2×C4⋊Dic61—21no—
105C2×C4⋊Dic61—21no—
106C2×C4⋊Dic61C2311yescharacteristic
107C2×C4⋊Dic61C2311yescharacteristic
108C2×#11758196—21no—
109C2×#11758196—21no—
110C4⋊C4×D61—22no—
111C4⋊C4×D61—22no—
112C2×C22⋊Dic61—21no—
113C2×#11758198—21no—
114C2×#11758198—21no—
115C2×#11758198—21no—
116C2×#11758198—21no—
117C22⋊C4×D61—28no—
118C2×C4×Dic61—21no—
119C2×C4×Dic61D411yescharacteristic
120C2×C4×Dic61D411yescharacteristic
121C2×C4×Dic61C2311yescharacteristic
122C42×D61—22no—
123C42×D61—22no—
124#14519711—22no—
125#14519710—22no—
126#14519702—22no—
127#14519700—22no—
128#14519699—22no—
129#14519698—22no—
130#14519697—22no—
131#14519697C2×C414yescomplemented
132#14519689—22no—
133#14519689C2×C414yescomplemented
134#14519688—22no—
135#14519684—21no—
136#14519684—21no—
137#14519684—21no—
138#14519684—21no—
139C22×D4×C61C2311yescharacteristic
140C23×C4×C61—21no—
141C22×C8×C61C2311yescharacteristic
142C22×C8×C61C2311yescharacteristic
143C4×D4×C61—22no—
144C4×D4×C61D414yes—
145C2×C4⋊C4×C61C2311yescharacteristic
146C2×C4⋊C4×C61C2311yescharacteristic
147C2×C4⋊C4×C61C2311yescharacteristic
148C2×C22⋊C4×C61—21no—
149C2×C42×C61—21no—
150C2×C42×C61C2311yescharacteristic
151#102×C61—22no—
152#102×C61C2×C414yescomplemented
153#97×C61—22no—
154#95×C61—21no—
155C24×C61—21no—
156C23×D61—24no—
157C23×D61—24no—
158C23×D61—21no—
159C23×D61—24no—
160C23×D61—42no—
161C23×D61—42no—
162C23×D61—42no—
163C23×D61—42no—
164C23×D61C2×D411yescharacteristic
165C2×D4×C61—21no—
166C2×D4×C61—21no—
167C2×D4×C61—21no—
168C2×D4×C61C22×C412yes—
169C2×D4×C61C2×D412yes—
170C2×D4×C61#4112yes—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—24no—
174C22×C4×C61—21no—
175C22×C4×C61—42no—
176C22×C4×C61—42no—
177C22×C4×C61C2×D411yescharacteristic
178C22×C4×C61C2×D411yescharacteristic
179C22×C4×C61C2411yescharacteristic
180C2×C22⋊D61—24no—
181C2×C22⋊D61—24no—
182C2×C22⋊D61—24no—
183C22×Dic61—24no—
184C22×Dic61—21no—
185C22×Dic61—21no—
186C22×Dic61—21no—
187C22×Dic61—42no—
188C22×Dic61—42no—
189C22×Dic61C2×D411yescharacteristic
190C22×Dic61C2×D411yescharacteristic
191C22×Dic61C2×D411yescharacteristic
192D4×D61—28no—
193D4×D61—28no—
194D4×D61—28no—
195D4×D61—28no—
196C2×D244—21no—
197C2×D244—21no—
198C2×D244—21no—
199C2×D244C22×C412yes—
200C2×D244C2×D412yes—
201C2×D244#4112yes—
202C2×C4×D61—22no—
203C2×C4×D61—22no—
204C2×C4×D61—21no—
205C2×C4×D61—21no—
206C2×C4×D61—21no—
207C2×C4×D61—21no—
208C2×C4×D61—22no—
209C2×C4×D61—24no—
210C2×C4×D61—24no—
211C2×C4×D61—22no—
212C2×C4×D61—24no—
213C2×C4×D61—22no—
214C2×C4×D61—432no—
215C2×C4×D61—41no—
216C2×C4×D61—42no—
217C2×C4×D61—42no—
218C2×C4×D61—42no—
219C2×C4×D61—42no—
220C2×C4×D61—42no—
221C2×C4×D61—42no—
222C2×C4×D61C22×C412yes—
223C2×C4×D61#4112yes—
224C2×Dic122—21no—
225C2×Dic122—21no—
226C2×Dic122—21no—
227C2×Dic122—21no—
228C2×Dic122—21no—
229C2×Dic122C22×C412yescomplemented
230C2×C8×C61—21no—
231C2×C8×C61—21no—
232C2×C8×C61—21no—
233C2×C8×C61—21no—
234C2×C8×C61—21no—
235C2×C8×C61C22×C412yescomplemented
236C4⋊C4×C61—21no—
237C4⋊C4×C61—21no—
238C4⋊C4×C61—21no—
239C4⋊C4×C61—21no—
240C4⋊C4×C61C22×C412yescomplemented
241C4⋊C4×C61C2×D412yes—
242C22⋊C4×C61—24no—
243C42×C61—42no—
244C42×C61C2×D412yes—
245C42×C61C2×D412yes—
246C22⋊Dic61—24no—
247#11758200—28no—
248#11758198—24no—
249#11758198—24no—
250#11758198—24no—
251#11758198—42no—
252C4⋊Dic61—21no—
253C4⋊Dic61—24no—
254C4⋊Dic61—21no—
255C4⋊Dic61—21no—
256C4⋊Dic61—42no—
257C4⋊Dic61C2×D412yes—
258#11758196—24no—
259#11758196—42no—
260C4×Dic61—22no—
261C4×Dic61—22no—
262C4×Dic61—21no—
263C4×Dic61—21no—
264C4×Dic61—42no—
265C2×#92418—21no—
266C2×#92418—21no—
267C2×#92418—21no—
268C2×#92418—21no—
269C2×#92418—21no—
270C2×#92418C22×C412yescomplemented
271#11758190—28no—
272C23×C61—22no—
273C23×C61—22no—
274C23×C61—22no—
275C23×C61—41no—
276C23×C61—41no—
277C23×C61—41no—
278C23×C61—41no—
279C23×C61C22×D411yescharacteristic
280C22×D61—21no—
281C22×D61—21no—
282C22×D61—21no—
283C22×D61—21no—
284C22×D61—216no—
285C22×D61—22no—
286C22×D61—22no—
287C22×D61—22no—
288C22×D61—48no—
289C22×D61—48no—
290C22×D61—48no—
291C22×D61—48no—
292C22×D61—48no—
293C22×D61—41no—
294C22×D61—41no—
295C22×D61—41no—
296C22×D61—41no—
297C22×D61—48no—
298C22×D61C4×D412yes—
299C22×D61AGL(1,ℤ/8)12yes—
300C22×D61#13712yes—
301D4×C61—22no—
302D4×C61—22no—
303D4×C61—22no—
304D4×C61C4×D414yes—
305C2×C4×C61—21no—
306C2×C4×C61—21no—
307C2×C4×C61—21no—
308C2×C4×C61—21no—
309C2×C4×C61—22no—
310C2×C4×C61—22no—
311C2×C4×C61—48no—
312C2×C4×C61—41no—
313C2×C4×C61—41no—
314C2×C4×C61—41no—
315C2×C4×C61—41no—
316C2×C4×C61—41no—
317C2×C4×C61—41no—
318C2×C4×C61—41no—
319C2×C4×C61#12012yes—
320C2×C4×C61#12012yes—
321C2×C4×C61C23×C411yescharacteristic
322C2×C4×C61C22×D411yescharacteristic
323C2×C4×C61C22×D411yescharacteristic
324C2×C4×C61C2×#4111yescharacteristic
325C2×C4×C61C2×#4111yescharacteristic
326C2×C4×C61C2×#4111yescharacteristic
327C22⋊D61—216no—
328C2×Dic61—21no—
329C2×Dic61—21no—
330C2×Dic61—21no—
331C2×Dic61—21no—
332C2×Dic61—22no—
333C2×Dic61—21no—
334C2×Dic61—22no—
335C2×Dic61—21no—
336C2×Dic61—21no—
337C2×Dic61—48no—
338C2×Dic61—41no—
339C2×Dic61—41no—
340C2×Dic61—41no—
341C2×Dic61—41no—
342C2×Dic61—41no—
343C2×Dic61—41no—
344C2×Dic61—41no—
345C2×Dic61C4×D412yes—
346C2×Dic61AGL(1,ℤ/8)12yes—
347D244—22no—
348D244—22no—
349D244—22no—
350D244C4×D414yes—
351C4×D61—28no—
352C4×D61—22no—
353C4×D61—22no—
354C4×D61—22no—
355C4×D61—22no—
356C4×D61—48no—
357C4×D61—44no—
358C4×D61—48no—
359C4×D61—48no—
360Dic122—22no—
361Dic122—22no—
362Dic122—41no—
363Dic122—41no—
364C8×C61—22no—
365C8×C61—41no—
366#92418—22no—
367#92418—41no—
368#21453—611nomaximal, Sylow
369C22×C61—24no—
370C22×C61—42no—
371C22×C61—42no—
372C22×C61—42no—
373C22×C61—42no—
374C22×C61—42no—
375C22×C61—42no—
376C22×C61C2×C4×D411yescharacteristic
377C22×C61C2×#12011yescharacteristic
378C22×C61#52511yescharacteristic
379C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
380C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
381C22×C61C2×#13711yescharacteristic
382C22×C61#57511yescharacteristic
383C2×D61—22no—
384C2×D61—22no—
385C2×D61—22no—
386C2×D61—22no—
387C2×D61—22no—
388C2×D61—22no—
389C2×D61—24no—
390C2×D61—432no—
391C2×D61—42no—
392C2×D61—42no—
393C2×D61—42no—
394C2×D61—42no—
395C2×D61—42no—
396C2×D61—42no—
397C2×D61#44014yescomplemented
398C4×C61—22no—
399C4×C61—22no—
400C4×C61—42no—
401C4×C61—42no—
402C4×C61—81no—
403C4×C61C2×C4×D411yescharacteristic
404C4×C61C2×C4×D411yescharacteristic
405C4×C61#52511yescharacteristic
406C4×C61#52511yescharacteristic
407Dic61—22no—
408Dic61—22no—
409Dic61—42no—
410Dic61—41no—
411Dic61—42no—
412Dic61—81no—
413C22×C4×D4—611no—
414C2×#450—611no—
415C2×#440—611no—
416C2×#440—611no—
417C4×C22⋊Q8—611no—
418#1877—611no—
419#1877—611no—
420#1872—611no—
421#1862—611no—
422#1862—611no—
423#1852—611no—
424#1786—611no—
425#1762—611no—
426#1762D6111yescharacteristic, complemented
427#1749—611no—
428C2×C61—44no—
429C2×C61C4×#12011yescharacteristic
430C2×C61C2×#44011yescharacteristic
431C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
432C2×C61#300311yescharacteristic
433C2×C61#300711yescharacteristic
434C2×C61#311011yescharacteristic
435C2×C61#311411yescharacteristic
436D61—24no—
437D61—44no—
438C23×D4—611no—
439C24×C4—1221no—
440C22×SD16—611no—
441C22×SD16—611no—
442C2×C22⋊Q8—611no—
443C2×C4×Q8—611no—
444C2×C4×D4—611no—
445C2×C4×D4—611no—
446C2×C4×D4—611no—
447C2×C4×D4—1221no—
448C2×C4×D4—1221no—
449C2×C4×D4—1224no—
450C2×C4×D4—1224no—
451C2×C4×D4C2×D6111yescharacteristic
452C22×C4⋊C4—611no—
453C22×C22⋊C4—1221no—
454C22×C42—611no—
455#450—618no—
456#440—1224no—
457#440—1224no—
458C2×#107—611no—
459C2×#107—611no—
460C2×#103—611no—
461C2×#103—611no—
462C2×#102—611no—
463C2×#102—611no—
464C2×#102—611no—
465C2×#102—611no—
466C2×#102C2×D6111yescharacteristic
467C2×#102C2×D6111yescharacteristic
468C2×C22⋊C8—611no—
469C2×C22⋊C8—611no—
470C2×#97—611no—
471C2×#97C2×D6111yescharacteristic, complemented
472#391—611no—
473#389—611no—
474#387—1221no—
475#385—1221no—
476#380—611no—
477C4×C4⋊C4—1221no—
478C4×C4⋊C4C2×D6111yescharacteristic, complemented
479C4×C22⋊C4—1221no—
480#340—611no—
481#340—611no—
482#340C2×D6111yescharacteristic, complemented
483#340C2×D6111yescharacteristic, complemented
484#336—611no—
485#336—611no—
486C61#2145311yescharacteristic, complemented, Sylow
487C25—1221no—
488C22×Q8—611no—
489C22×D4—614no—
490C22×D4—611no—
491C22×D4—1222no—
492C22×D4—1221no—
493C22×D4—1222no—
494C22×D4—1222no—
495C22×D4—1222no—
496C22×D4—1222no—
497C22×D4C22×D6111yescharacteristic
498C23×C4—21no—
499C23×C4—611no—
500C23×C4—611no—
501C23×C4—611no—
502C23×C4—1221no—
503C23×C4—1221no—
504C23×C4—1228no—
505C23×C4—1221no—
506C23×C4—1221no—
507C23×C4—2444no—
508C23×C4—2444no—
509C2×SD16—614no—
510C2×SD16—614no—
511C2×SD16—1222no—
512C2×SD16—1222no—
513C2×SD16—1222no—
514C2×SD16—1222no—
515C22×C8—611no—
516C22×C8—611no—
517C22×C8C22×D6111yescharacteristic
518C22×C8C22×D6111yescharacteristic
519C22⋊Q8—614no—
520C22⋊Q8—1222no—
521C4×Q8—1222no—
522C4×Q8—1222no—
523C4×D4—22no—
524C4×D4—614no—
525C4×D4—1228no—
526C4×D4—1222no—
527C4×D4—1222no—
528C4×D4—1228no—
529C4×D4—1222no—
530C4×D4—1222no—
531C4×D4—1222no—
532C4×D4D24414yes—
533C2×C4⋊C4—611no—
534C2×C4⋊C4—611no—
535C2×C4⋊C4—1222no—
536C2×C4⋊C4—1221no—
537C2×C4⋊C4—1221no—
538C2×C4⋊C4—1222no—
539C2×C4⋊C4—1221no—
540C2×C4⋊C4—1221no—
541C2×C4⋊C4C22×D6111yescharacteristic
542C2×C4⋊C4C22×D6111yescharacteristic
543C2×C4⋊C4C22×D6111yescharacteristic
544C2×C22⋊C4—21no—
545C2×C22⋊C4—1228no—
546C2×C22⋊C4—1221no—
547C2×C22⋊C4—1221no—
548C2×C22⋊C4—1221no—
549C2×C22⋊C4—1221no—
550C2×C22⋊C4—1221no—
551C2×C42—21no—
552C2×C42—611no—
553C2×C42—611no—
554C2×C42—611no—
555C2×C42—1222no—
556C2×C42—1222no—
557C2×C42—1221no—
558C2×C42C22×D6111yescharacteristic
559#107—1222no—
560#107—1222no—
561#103—1222no—
562#103—1222no—
563#102—22no—
564#102—614no—
565#102—1222no—
566#102—1222no—
567#102—1222no—
568#102C4×D6114yescomplemented
569C22⋊C8—614no—
570C22⋊C8—1222no—
571#97—22no—
572#97—1222no—
573#95—21no—
574#95—1221no—
575#95—1221no—
576#95—1221no—
577#95—1221no—
578C24—21no—
579C24—611no—
580C24—1224no—
581C24—1224no—
582C24—1224no—
583C24—1221no—
584C24—2442no—
585C24—2442no—
586C24—2442no—
587C24—2442no—
588C2×Q8—612no—
589C2×Q8—1221no—
590C2×Q8—1221no—
591C2×Q8—1221no—
592C2×Q8—1221no—
593C2×Q8—1221no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—612no—
598C2×D4—612no—
599C2×D4—612no—
600C2×D4—1224no—
601C2×D4—1228no—
602C2×D4—1228no—
603C2×D4—1228no—
604C2×D4—1224no—
605C2×D4—1224no—
606C2×D4—1228no—
607C2×D4—1221no—
608C2×D4—1221no—
609C2×D4—1221no—
610C2×D4C2×C4×D6112yes—
611C2×D4C2×D24412yes—
612C2×D4#1175822212yes—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—24no—
616C22×C4—21no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4—611no—
620C22×C4—611no—
621C22×C4—612no—
622C22×C4—612no—
623C22×C4—611no—
624C22×C4—1222no—
625C22×C4—1222no—
626C22×C4—1222no—
627C22×C4—1224no—
628C22×C4—1224no—
629C22×C4—1221no—
630C22×C4—1221no—
631C22×C4—1221no—
632C22×C4—1221no—
633C22×C4—1222no—
634C22×C4—1224no—
635C22×C4—1221no—
636C22×C4—1221no—
637C22×C4—1222no—
638C22×C4—1224no—
639C22×C4—1221no—
640C22×C4—2441no—
641C22×C4—2442no—
642C22×C4—2442no—
643C22×C4—2442no—
644C22×C4—24432no—
645C22×C4—2442no—
646C22×C4—2442no—
647C22×C4—2442no—
648C22×C4—2442no—
649C22×C4—2442no—
650C22×C4D4×D6111yescharacteristic
651C22×C4D4×D6111yescharacteristic
652C22×C4C23×D6111yescharacteristic
653SD16—1228no—
654SD16—1228no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—612no—
661C2×C8—1221no—
662C2×C8—1221no—
663C2×C8—1221no—
664C2×C8—1221no—
665C2×C8—1221no—
666C2×C8C2×C4×D6112yescomplemented
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—612no—
672C4⋊C4—1224no—
673C4⋊C4—1224no—
674C4⋊C4—1221no—
675C4⋊C4—1221no—
676C4⋊C4—1221no—
677C4⋊C4—2442no—
678C4⋊C4—2442no—
679C4⋊C4C2×C4×D6112yescomplemented
680C4⋊C4C2×D24412yes—
681C22⋊C4—24no—
682C22⋊C4—1224no—
683C22⋊C4—1224no—
684C22⋊C4—1224no—
685C22⋊C4—1224no—
686C22⋊C4—2442no—
687C42—42no—
688C42—1221no—
689C42—1221no—
690C42—1222no—
691C42—1222no—
692C42—2442no—
693C42C2×D24412yes—
694C42D4×D6112yes—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—612no—
703C23—612no—
704C23—612no—
705C23—12216no—
706C23—1221no—
707C23—1221no—
708C23—1221no—
709C23—1221no—
710C23—1222no—
711C23—1222no—
712C23—1222no—
713C23—2448no—
714C23—2448no—
715C23—2448no—
716C23—2448no—
717C23—2448no—
718C23—2448no—
719C23—2441no—
720C23—2441no—
721C23—2441no—
722C23—2441no—
723C23C2×D4×D6111yescharacteristic
724Q8—1222no—
725Q8—1222no—
726Q8—2441no—
727Q8—2441no—
728D4—22no—
729D4—22no—
730D4—22no—
731D4—614no—
732D4—12216no—
733D4—1222no—
734D4—1222no—
735D4—1222no—
736D4C4×D24414yes—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—48no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—612no—
752C2×C4—612no—
753C2×C4—1228no—
754C2×C4—1221no—
755C2×C4—1221no—
756C2×C4—1221no—
757C2×C4—1221no—
758C2×C4—1222no—
759C2×C4—1222no—
760C2×C4—1222no—
761C2×C4—1222no—
762C2×C4—1222no—
763C2×C4—1221no—
764C2×C4—1222no—
765C2×C4—1221no—
766C2×C4—1221no—
767C2×C4—2444no—
768C2×C4—2448no—
769C2×C4—2448no—
770C2×C4—2448no—
771C2×C4—2448no—
772C2×C4—2441no—
773C2×C4—2441no—
774C2×C4—2441no—
775C2×C4—2441no—
776C2×C4—2441no—
777C2×C4—2441no—
778C2×C4—2441no—
779C2×C4#1451974712yes—
780C2×C4#1451974712yes—
781C2×C4C22×C4×D6111yescharacteristic
782C2×C4C2×D4×D6111yescharacteristic
783C2×C4C22×D24411yescharacteristic
784C2×C4#41×D6111yescharacteristic
785C2×C4#41×D6111yescharacteristic
786C2×C4C2×#1175822211yescharacteristic
787C8—22no—
788C8—41no—
789C8—1222no—
790C8—2441no—
791C22—24no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—614no—
799C22—1222no—
800C22—1222no—
801C22—1222no—
802C22—1222no—
803C22—1222no—
804C22—1222no—
805C22—1224no—
806C22—24432no—
807C22—2442no—
808C22—2442no—
809C22—2442no—
810C22—2442no—
811C22—2442no—
812C22—2442no—
813C22C4×D4×D6111yescharacteristic
814C22C2×#1451974711yescharacteristic
815C22#1684027111yescharacteristic
816C22AGL(1,ℤ/8)×D6111yescharacteristic
817C22AGL(1,ℤ/8)×D6111yescharacteristic
818C22#137×D6111yescharacteristic
819C22#1684055811yescharacteristic
820C4—22no—
821C4—22no—
822C4—42no—
823C4—42no—
824C4—81no—
825C4—1222no—
826C4—1222no—
827C4—4881no—
828C4—2442no—
829C4—2442no—
830C4—2441no—
831C4C4×D4×D6111yescharacteristic
832C4C2×C4×D24411yescharacteristic
833C4#1684027111yescharacteristic
834C4#1684027411yescharacteristic
835C2—44no—
836C2—1224no—
837C2—2444no—
838C2C4×#1451974711yescharacteristic
839C2#440×D6111yescharacteristic
840C2#2145463011yescharacteristic
841C2#2145504811yescharacteristic
842C2#2145508011yescharacteristic
843C2#2145591611yescharacteristic
844C2#2145595511yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1762C2
socleC23×C61C22×D4
prime radicalC22×D4×D61C22
cosocleC22×C4×C61C24
hypercenter#1762D61
hypocenterC61#21453
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1762

Complements

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

NH ≅ G/Ntype
3. C2×#16839864C2semidirect
4. C2×#16839862C2semidirect
5. C4×#14519757C2semidirect
6. #21446154C2semidirect
7. #21446151C2semidirect
8. #21446125C2semidirect
9. #21446068C2semidirect
10. #21446067C2semidirect
11. #21446008C2semidirect
13. #21445647C2semidirect
14. #21445582C2semidirect
15. C61×#1762C2semidirect
21. C2×C4×Dic122C22semidirect
32. #16839914C4semidirect
35. C2×#14519711C22semidirect
36. C2×#14519710C22semidirect
37. C2×#14519702C22semidirect
38. C2×#14519700C22semidirect
45. C2×#14519688C22semidirect
46. #16839667C22semidirect
47. #16839661C22semidirect
53. #16839524C22semidirect
54. #16839524C22semidirect
55. #16839516C22semidirect
56. #16839516C22semidirect
60. C2×#97×C61C22semidirect
61. C4×C4⋊C4×C61C22semidirect
62. C61×#340C22semidirect
63. C61×#340C22semidirect
86. C2×#11758190C2×C4semidirect
89. C2×#11758200C2×C4semidirect
93. #14519757C2×C4semidirect
131. #14519697C2×C4semidirect
133. #14519689C2×C4semidirect
152. #102×C61C2×C4semidirect
229. C2×Dic122C22×C4semidirect
235. C2×C8×C61C22×C4semidirect
240. C4⋊C4×C61C22×C4semidirect
270. C2×#92418C22×C4semidirect
397. C2×D61#440semidirect
426. #1762D61semidirect
471. C2×#97C2×D61semidirect
478. C4×C4⋊C4C2×D61semidirect
482. #340C2×D61semidirect
483. #340C2×D61semidirect
486. C61#21453semidirect
568. #102C4×D61semidirect
666. C2×C8C2×C4×D61semidirect
679. C4⋊C4C2×C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×D612
C2×#168399142
C2×#168398642
C2×#168398622
C4×#145197572
#214461542
#214461512
#214461252
#214460682
#214460672
#214460082
#214457482
#214456472
#214455822
C61×#17622
#2145361