Finite Group Databasebeta

← D61×#1478 #29646367

Subgroups — D61×#1478 #29646367

Order 15616.

1714 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D61C211yesmaximal, characteristic
2#431×D61C211yesmaximal, characteristic, complemented
3#431×D61C211yesmaximal, characteristic, complemented
4#21444211C211yesmaximal, characteristic, complemented
5#21444210C211yesmaximal, characteristic, complemented
6#21444209C211yesmaximal, characteristic, complemented
7#21444208C214yesmaximal, complemented
8D4⋊C8×D61C214yesmaximal, complemented
9C61×#1478C211yesmaximal, characteristic, complemented
10C22×D4×D61C411yescharacteristic
11C23×C4×D61—21no—
12C2×C4×D244C2211yescharacteristic
13C2×D4×Dic61C411yescharacteristic
14C2×#14519739C411yescharacteristic
15C2×C4×C22⋊D61—21no—
16C2×#14519737—21no—
17C4×D4×D61—21no—
18C4×D4×D61—21no—
19C4×D4×D61—21no—
20C4×D4×D61—21no—
21C4×D4×D61C412yes—
22C4×D4×D61C412yes—
23C4×D4×D61C2212yes—
24C4×D4×D61C2212yes—
25C2×C4⋊C4×D61C411yescharacteristic
26C2×C22⋊C4×D61—21no—
27C2×C42×D61C2211yescharacteristic
28#16839815C2211yescharacteristic, complemented
29#16839815C2211yescharacteristic, complemented
30#16839814—21no—
31#16839814C2212yescomplemented
32#16839813—21no—
33#16839813C2212yescomplemented
34#16839812—21no—
35#16839812—21no—
36C4⋊C8×D61—21no—
37C4⋊C8×D61C2212yescomplemented
38C22⋊C8×D61—21no—
39C22⋊C8×D61—21no—
40C4×C8×D61—21no—
41C4×C8×D61C2212yescomplemented
42#16839491C2214yescomplemented
43D4⋊#92418C2214yescomplemented
44#16839489C2214yescomplemented
45C2×C4×D4×C61C2211yescharacteristic
46C61×#431C2211yescharacteristic, complemented
47C61×#431C2211yescharacteristic, complemented
48C61×D4⋊C8C2214yescomplemented
49C24×D61—21no—
50C22×D244C2×C411yescharacteristic
51C22×C22⋊D61—21no—
52C2×D4×D61—21no—
53C2×D4×D61—21no—
54C2×D4×D61—24no—
55C2×D4×D61C818yescomplemented
56C2×D4×D61C2×C412yes—
57C2×D4×D61C2×C412yes—
58C23×Dic61—21no—
59C22×C4×D61—21no—
60C22×C4×D61—21no—
61C22×C4×D61—21no—
62C22×C4×D61—22no—
63C22×C4×D61—22no—
64C22×C4×D61—22no—
65C22×C4×D61—22no—
66C22×C4×D61—48no—
67C22×C4×D61C2×C411yescharacteristic
68C22×C4×D61D411yescharacteristic
69C22×C4×D61D411yescharacteristic
70C2×C8×D61—22no—
71C2×C8×D61—22no—
72C4×D244—21no—
73C4×D244—21no—
74C4×D244C2×C412yes—
75C4×D244C2312yes—
76D4×Dic61—21no—
77D4×Dic61—21no—
78D4×Dic61C2×C412yes—
79D4×Dic61C2×C412yes—
80#14519739—21no—
81#14519739—21no—
82#14519739C2×C412yes—
83#14519739C2×C412yes—
84C4×C22⋊D61—22no—
85C4×C22⋊D61—22no—
86C4×C22⋊D61—22no—
87C4×C22⋊D61—22no—
88#14519737—22no—
89#14519737—22no—
90#14519737—22no—
91#14519737—22no—
92C2×C4⋊Dic61C2×C411yescharacteristic
93C2×#11758196—21no—
94C4⋊C4×D61—21no—
95C4⋊C4×D61—21no—
96C4⋊C4×D61C2×C412yes—
97C4⋊C4×D61C2×C412yes—
98C2×C22⋊Dic61—21no—
99C2×#11758198—21no—
100C2×#11758198—21no—
101C22⋊C4×D61—22no—
102C22⋊C4×D61—22no—
103C22⋊C4×D61—22no—
104C22⋊C4×D61—22no—
105C2×C4×Dic61C2×C411yescharacteristic
106C2×C4×Dic61D411yescharacteristic
107C2×C4×Dic61D411yescharacteristic
108C42×D61C2×C411yescharacteristic
109C42×D61C2×C411yescharacteristic
110C42×D61D411yescharacteristic
111C42×D61D411yescharacteristic
112C42×D61D411yescharacteristic
113C42×D61D411yescharacteristic
114C42×D61C2311yescharacteristic
115C42×D61C2311yescharacteristic
116C4⋊#92418—21no—
117C4⋊#92418C2312yescomplemented
118#14519706—22no—
119#14519706—22no—
120C22⋊#92418—21no—
121C22⋊#92418—21no—
122#14519689—22no—
123#14519689—22no—
124C4×#92418—21no—
125C4×#92418C2312yescomplemented
126C8×Dic61—22no—
127C8×Dic61—22no—
128C22×D4×C61C2×C411yescharacteristic
129C23×C4×C61—21no—
130C4×D4×C61—21no—
131C4×D4×C61—21no—
132C4×D4×C61C2×C412yes—
133C4×D4×C61C2312yes—
134C2×C4⋊C4×C61C2×C411yescharacteristic
135C2×C22⋊C4×C61—21no—
136C2×C42×C61C2311yescharacteristic
137C4⋊C8×C61—21no—
138C4⋊C8×C61C2312yescomplemented
139C22⋊C8×C61—21no—
140C22⋊C8×C61—21no—
141C4×C8×C61—21no—
142C4×C8×C61C2312yescomplemented
143C24×C61—21no—
144C23×D61—21no—
145C23×D61—28no—
146C23×D61—22no—
147C23×D61—22no—
148C23×D61—44no—
149C23×D61—44no—
150C23×D61C22⋊C411yescharacteristic
151C2×D4×C61—21no—
152C2×D4×C61—22no—
153C2×D4×C61C2×C814yescomplemented
154C2×D4×C61C22×C412yes—
155C22×C4×C61—21no—
156C22×C4×C61—22no—
157C22×C4×C61—22no—
158C22×C4×C61—44no—
159C22×C4×C61C22×C411yescharacteristic
160C22×C4×C61C2×D411yescharacteristic
161C22×C4×C61C2×D411yescharacteristic
162C2×C22⋊D61—28no—
163C2×C22⋊D61—22no—
164C2×C22⋊D61—22no—
165C22×Dic61—21no—
166C22×Dic61—22no—
167C22×Dic61—22no—
168C22×Dic61—44no—
169C22×Dic61C22⋊C411yescharacteristic
170C22×Dic61C22⋊C411yescharacteristic
171C22×Dic61C22⋊C411yescharacteristic
172D4×D61—28no—
173D4×D61—28no—
174D4×D61—24no—
175D4×D61—24no—
176D4×D61C2×C818yes—
177D4×D61C2×C818yescomplemented
178C2×D244—21no—
179C2×D244—22no—
180C2×D244C2×C814yescomplemented
181C2×D244C22×C412yes—
182C2×C4×D61—24no—
183C2×C4×D61—22no—
184C2×C4×D61—22no—
185C2×C4×D61—22no—
186C2×C4×D61—22no—
187C2×C4×D61—22no—
188C2×C4×D61—22no—
189C2×C4×D61—42no—
190C2×C4×D61—48no—
191C2×C4×D61—48no—
192C2×C4×D61—48no—
193C2×C4×D61—44no—
194C2×C4×D61—44no—
195C2×C4×D61—44no—
196C2×C4×D61—48no—
197C2×C4×D61C22⋊C411yescharacteristic
198C2×C4×D61C22⋊C411yescharacteristic
199C2×C4×D61C22⋊C411yescharacteristic
200C2×C4×D61C22⋊C411yescharacteristic
201C2×C4×D61C22⋊C411yescharacteristic
202C2×C4×D61C22⋊C411yescharacteristic
203C2×C4×D61C2×C814yes—
204C2×C4×D61M1614yes—
205C2×C4×D61C22×C411yescharacteristic
206C2×C4×D61C22×C411yescharacteristic
207C2×C4×D61C2×D411yescharacteristic
208C2×C4×D61C2×D411yescharacteristic
209C2×C4×D61C2×D411yescharacteristic
210C2×C4×D61C2×D411yescharacteristic
211C2×C8×C61—22no—
212C2×C8×C61—22no—
213C4⋊C4×C61—21no—
214C4⋊C4×C61C22×C412yes—
215C22⋊C4×C61—22no—
216C22⋊C4×C61—22no—
217C42×C61C22×C411yescharacteristic
218C42×C61C2×D411yescharacteristic
219C42×C61C2×D411yescharacteristic
220C42×C61C2411yescharacteristic
221C22⋊Dic61—22no—
222C22⋊Dic61—22no—
223#11758198—22no—
224#11758198—22no—
225#11758198—22no—
226#11758198—22no—
227C4⋊Dic61—21no—
228C4⋊Dic61C22×C412yes—
229#11758196—22no—
230#11758196—22no—
231C4×Dic61C22⋊C411yescharacteristic
232C4×Dic61C22⋊C411yescharacteristic
233C4×Dic61C22⋊C411yescharacteristic
234C4×Dic61C22⋊C411yescharacteristic
235C4×Dic61C22⋊C411yescharacteristic
236C4×Dic61C22⋊C411yescharacteristic
237C4×Dic61C22×C411yescharacteristic
238C4×Dic61C22×C411yescharacteristic
239C4×Dic61C2×D411yescharacteristic
240C4×Dic61C2×D411yescharacteristic
241C4×Dic61C2×D411yescharacteristic
242C4×Dic61C2×D411yescharacteristic
243C2×#92418—22no—
244C2×#92418—22no—
245C8×D61—44no—
246C8×D61—44no—
247C23×C61—22no—
248C23×C61—24no—
249C23×C61—42no—
250C23×C61—42no—
251C23×C61C2×C22⋊C411yescharacteristic
252C22×D61—22no—
253C22×D61—22no—
254C22×D61—22no—
255C22×D61—24no—
256C22×D61—28no—
257C22×D61—28no—
258C22×D61—44no—
259C22×D61—44no—
260C22×D61—432no—
261C22×D61—42no—
262C22×D61—42no—
263C22×D61—44no—
264C22×D61—44no—
265C22×D61C22⋊C814yes—
266C22×D61C2×C22⋊C411yescharacteristic
267C22×D61C2×C22⋊C411yescharacteristic
268D4×C61—22no—
269D4×C61—24no—
270D4×C61C22×C814yes—
271C2×C4×C61—22no—
272C2×C4×C61—22no—
273C2×C4×C61—41no—
274C2×C4×C61—44no—
275C2×C4×C61—42no—
276C2×C4×C61—44no—
277C2×C4×C61C2×C22⋊C411yescharacteristic
278C2×C4×C61C2×C22⋊C411yescharacteristic
279C2×C4×C61C2×C22⋊C411yescharacteristic
280C2×C4×C61C22×C812yes—
281C2×C4×C61C2×M1612yes—
282C2×C4×C61C23×C411yescharacteristic
283C2×C4×C61C22×D411yescharacteristic
284C2×C4×C61C22×D411yescharacteristic
285C22⋊D61—28no—
286C22⋊D61—28no—
287C2×Dic61—22no—
288C2×Dic61—22no—
289C2×Dic61—41no—
290C2×Dic61—44no—
291C2×Dic61—42no—
292C2×Dic61—44no—
293C2×Dic61C22⋊C814yes—
294C2×Dic61C2×C22⋊C411yescharacteristic
295C2×Dic61C2×C22⋊C411yescharacteristic
296C2×Dic61C2×C22⋊C411yescharacteristic
297C2×Dic61C2×C22⋊C411yescharacteristic
298C2×Dic61C2×C22⋊C411yescharacteristic
299C2×Dic61C2×C22⋊C411yescharacteristic
300D244—22no—
301D244—24no—
302D244C22×C814yes—
303C4×D61—22no—
304C4×D61—22no—
305C4×D61—22no—
306C4×D61—22no—
307C4×D61—22no—
308C4×D61—41no—
309C4×D61—41no—
310C4×D61—44no—
311C4×D61—44no—
312C4×D61—44no—
313C4×D61—44no—
314C4×D61—44no—
315C4×D61—44no—
316C4×D61C22⋊C814yes—
317C4×D61C22⋊C814yes—
318C4×D61C22×C812yes—
319C4×D61C22×C812yes—
320C4×D61C2×M1612yes—
321C4×D61C2×M1612yes—
322C4×D61AGL(1,ℤ/8)14yes—
323C8×C61—42no—
324C8×C61—42no—
325#92418—42no—
326#92418—42no—
327C2×#1478—611nomaximal, Sylow
328C22×C61—21no—
329C22×C61—21no—
330C22×C61—24no—
331C22×C61—48no—
332C22×C61—42no—
333C22×C61—42no—
334C22×C61C2×C22⋊C812yes—
335C22×C61C22×C22⋊C411yescharacteristic
336C2×D61—21no—
337C2×D61—21no—
338C2×D61—28no—
339C2×D61—24no—
340C2×D61—416no—
341C2×D61—48no—
342C2×D61—42no—
343C2×D61—42no—
344C2×D61—416no—
345C2×D61C2×C22⋊C812yes—
346C2×D61C2×C22⋊C812yes—
347C2×D61#41812yes—
348C2×D61#42112yes—
349C4×C61—21no—
350C4×C61—21no—
351C4×C61—21no—
352C4×C61—42no—
353C4×C61C2×C22⋊C812yes—
354C4×C61C23×C811yescharacteristic
355C4×C61C22×M1611yescharacteristic
356C4×C61C2×AGL(1,ℤ/8)12yes—
357Dic61—21no—
358Dic61—21no—
359Dic61—21no—
360Dic61—42no—
361Dic61C2×C22⋊C812yes—
362Dic61C2×C22⋊C812yes—
363Dic61#41812yes—
364C22×C4×D4—611no—
365C2×#431—611no—
366C2×#431—611no—
367#1478—611no—
368#1478—611no—
369#1478—614no—
370#1478—611no—
371#1478D6111yescharacteristic, direct product factor
372C2×D4⋊C8—614no—
373C2×C61—22no—
374C2×C61—44no—
375C2×C61C22×C22⋊C811yescharacteristic
376C2×C61C2×#41811yescharacteristic
377C2×C61C2×#42111yescharacteristic
378D61—22no—
379D61—44no—
380D61#147814yesdirect product factor
381C23×D4—611no—
382C24×C4—1221no—
383C2×C4×D4—611no—
384C2×C4×D4—612no—
385C2×C4×D4—612no—
386C2×C4×D4—612no—
387C2×C4×D4—612no—
388C2×C4×D4—611no—
389C2×C4×D4—611no—
390C2×C4×D4—1221no—
391C2×C4×D4—1221no—
392C2×C4×D4—1221no—
393C2×C4×D4—1221no—
394C2×C4×D4—1221no—
395C2×C4×D4—1221no—
396C2×C4×D4C2×D6111yescharacteristic
397C22×C4⋊C4—611no—
398C22×C22⋊C4—1221no—
399C22×C42—611no—
400#431—611no—
401#431—612no—
402#431—611no—
403#431—612no—
404#431—1221no—
405#431—1221no—
406#431—1221no—
407#431—1221no—
408#431C2×D6111yescharacteristic, complemented
409#431C2×D6111yescharacteristic, complemented
410C2×C4⋊C8—612no—
411C2×C4⋊C8—1221no—
412C2×C22⋊C8—1221no—
413C2×C22⋊C8—1221no—
414C2×C4×C8—612no—
415C2×C4×C8—1221no—
416D4⋊C8—614no—
417D4⋊C8—614no—
418D4⋊C8—614no—
419D4⋊C8C2×D6114yescomplemented
420C61C2×#147811yescharacteristic, complemented, Sylow
421C25—1221no—
422C22×D4—618no—
423C22×D4—612no—
424C22×D4—612no—
425C22×D4—611no—
426C22×D4—1221no—
427C22×D4—1221no—
428C22×D4—1224no—
429C22×D4—1221no—
430C22×D4C4×D6111yescharacteristic
431C23×C4—21no—
432C23×C4—611no—
433C23×C4—611no—
434C23×C4—611no—
435C23×C4—1221no—
436C23×C4—1222no—
437C23×C4—1222no—
438C23×C4—1222no—
439C23×C4—1222no—
440C23×C4—1221no—
441C23×C4—1221no—
442C23×C4—1221no—
443C23×C4—2448no—
444C22×C8—1222no—
445C22×C8—1222no—
446C4×D4—21no—
447C4×D4—21no—
448C4×D4—612no—
449C4×D4—612no—
450C4×D4—612no—
451C4×D4—612no—
452C4×D4—612no—
453C4×D4—612no—
454C4×D4—1222no—
455C4×D4—1222no—
456C4×D4—1222no—
457C4×D4—1222no—
458C4×D4—1221no—
459C4×D4—1221no—
460C4×D4—1222no—
461C4×D4—1222no—
462C4×D4—1222no—
463C4×D4—1222no—
464C4×D4—1221no—
465C4×D4—1221no—
466C4×D4—1221no—
467C4×D4—1221no—
468C4×D4C4×D6112yes—
469C4×D4C22×D6112yes—
470C2×C4⋊C4—611no—
471C2×C4⋊C4—612no—
472C2×C4⋊C4—612no—
473C2×C4⋊C4—1221no—
474C2×C4⋊C4—1221no—
475C2×C4⋊C4—1221no—
476C2×C4⋊C4C4×D6111yescharacteristic
477C2×C22⋊C4—21no—
478C2×C22⋊C4—1222no—
479C2×C22⋊C4—1222no—
480C2×C22⋊C4—1222no—
481C2×C22⋊C4—1222no—
482C2×C22⋊C4—1221no—
483C2×C22⋊C4—1221no—
484C2×C22⋊C4—1221no—
485C2×C42—611no—
486C2×C42—611no—
487C2×C42—611no—
488C2×C42—611no—
489C2×C42—611no—
490C2×C42—611no—
491C2×C42—611no—
492C2×C42—611no—
493C2×C42—611no—
494C2×C42—611no—
495C2×C42—611no—
496C2×C42C22×D6111yescharacteristic
497C4⋊C8—21no—
498C4⋊C8—612no—
499C4⋊C8—1222no—
500C4⋊C8—1222no—
501C4⋊C8—1221no—
502C4⋊C8C22×D6112yescomplemented
503C22⋊C8—21no—
504C22⋊C8—21no—
505C22⋊C8—1222no—
506C22⋊C8—1222no—
507C22⋊C8—1221no—
508C22⋊C8—1221no—
509C4×C8—21no—
510C4×C8—612no—
511C4×C8—1222no—
512C4×C8—1222no—
513C4×C8—1221no—
514C4×C8C22×D6112yescomplemented
515C24—21no—
516C24—611no—
517C24—1222no—
518C24—1222no—
519C24—1228no—
520C24—1221no—
521C24—2444no—
522C24—2444no—
523C2×D4—21no—
524C2×D4—22no—
525C2×D4—618no—
526C2×D4—618no—
527C2×D4—612no—
528C2×D4—614no—
529C2×D4—1228no—
530C2×D4—1228no—
531C2×D4—1224no—
532C2×D4—1224no—
533C2×D4—1222no—
534C2×D4—1222no—
535C2×D4—1228no—
536C2×D4—1221no—
537C2×D4—1222no—
538C2×D4C8×D6114yescomplemented
539C2×D4C2×C4×D6112yes—
540C22×C4—21no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—44no—
544C22×C4—611no—
545C22×C4—611no—
546C22×C4—611no—
547C22×C4—611no—
548C22×C4—611no—
549C22×C4—611no—
550C22×C4—614no—
551C22×C4—614no—
552C22×C4—611no—
553C22×C4—611no—
554C22×C4—611no—
555C22×C4—611no—
556C22×C4—611no—
557C22×C4—611no—
558C22×C4—611no—
559C22×C4—611no—
560C22×C4—611no—
561C22×C4—1224no—
562C22×C4—1222no—
563C22×C4—1222no—
564C22×C4—1222no—
565C22×C4—1222no—
566C22×C4—1222no—
567C22×C4—1222no—
568C22×C4—1221no—
569C22×C4—1222no—
570C22×C4—1222no—
571C22×C4—2444no—
572C22×C4—2448no—
573C22×C4—2442no—
574C22×C4—2448no—
575C22×C4—2448no—
576C22×C4—2444no—
577C22×C4—2448no—
578C22×C4—2444no—
579C22×C4—2444no—
580C22×C4C2×C4×D6111yescharacteristic
581C22×C4D4×D6111yescharacteristic
582C22×C4D4×D6111yescharacteristic
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—1222no—
586C2×C8—1222no—
587C2×C8—2444no—
588C2×C8—2444no—
589C4⋊C4—21no—
590C4⋊C4—612no—
591C4⋊C4—1222no—
592C4⋊C4—1222no—
593C4⋊C4—1221no—
594C4⋊C4C2×C4×D6112yes—
595C22⋊C4—22no—
596C22⋊C4—22no—
597C22⋊C4—1222no—
598C22⋊C4—1222no—
599C22⋊C4—1222no—
600C22⋊C4—1222no—
601C22⋊C4—1222no—
602C22⋊C4—1222no—
603C42—611no—
604C42—611no—
605C42—611no—
606C42—611no—
607C42—611no—
608C42—611no—
609C42—611no—
610C42—611no—
611C42—611no—
612C42—611no—
613C42—611no—
614C42—611no—
615C42C2×C4×D6111yescharacteristic
616C42D4×D6111yescharacteristic
617C42D4×D6111yescharacteristic
618C42C23×D6111yescharacteristic
619C23—22no—
620C23—24no—
621C23—42no—
622C23—42no—
623C23—611no—
624C23—611no—
625C23—614no—
626C23—1222no—
627C23—1222no—
628C23—1228no—
629C23—1228no—
630C23—1222no—
631C23—1224no—
632C23—2442no—
633C23—2442no—
634C23—2444no—
635C23—2444no—
636C23—2444no—
637C23—24432no—
638C23—2444no—
639C23C22⋊C4×D6111yescharacteristic
640D4—24no—
641D4—22no—
642D4—614no—
643D4—1228no—
644D4—1228no—
645D4—1224no—
646D4—1222no—
647D4C2×C8×D6114yes—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—41no—
651C2×C4—44no—
652C2×C4—42no—
653C2×C4—44no—
654C2×C4—611no—
655C2×C4—611no—
656C2×C4—611no—
657C2×C4—614no—
658C2×C4—614no—
659C2×C4—614no—
660C2×C4—612no—
661C2×C4—612no—
662C2×C4—612no—
663C2×C4—612no—
664C2×C4—614no—
665C2×C4—611no—
666C2×C4—611no—
667C2×C4—611no—
668C2×C4—1222no—
669C2×C4—1222no—
670C2×C4—1222no—
671C2×C4—1222no—
672C2×C4—1222no—
673C2×C4—1222no—
674C2×C4—1222no—
675C2×C4—2441no—
676C2×C4—2441no—
677C2×C4—2444no—
678C2×C4—2444no—
679C2×C4—2444no—
680C2×C4—2444no—
681C2×C4—2444no—
682C2×C4—2444no—
683C2×C4—2441no—
684C2×C4—2444no—
685C2×C4—2442no—
686C2×C4—2444no—
687C2×C4C22⋊C4×D6111yescharacteristic
688C2×C4C22⋊C4×D6111yescharacteristic
689C2×C4C22⋊C4×D6111yescharacteristic
690C2×C4C2×C8×D6112yes—
691C2×C4M16×D6112yes—
692C2×C4C22×C4×D6111yescharacteristic
693C2×C4C2×D4×D6111yescharacteristic
694C2×C4C2×D4×D6111yescharacteristic
695C8—42no—
696C8—42no—
697C8—2442no—
698C8—2442no—
699C22—21no—
700C22—21no—
701C22—24no—
702C22—48no—
703C22—42no—
704C22—42no—
705C22—612no—
706C22—612no—
707C22—612no—
708C22—612no—
709C22—1228no—
710C22—1221no—
711C22—1221no—
712C22—1224no—
713C22—2448no—
714C22—24416no—
715C22—24416no—
716C22—2442no—
717C22—2442no—
718C22C22⋊C8×D6112yes—
719C22C2×C22⋊C4×D6111yescharacteristic
720C4—21no—
721C4—21no—
722C4—21no—
723C4—42no—
724C4—612no—
725C4—612no—
726C4—612no—
727C4—1221no—
728C4—1221no—
729C4—1221no—
730C4—2442no—
731C4C22⋊C8×D6112yes—
732C4C22×C8×D6111yescharacteristic
733C4C2×M16×D6111yescharacteristic
734C4AGL(1,ℤ/8)×D6112yes—
735C2—22no—
736C2—44no—
737C2—614no—
738C2—1222no—
739C2—2444no—
740C2C2×C22⋊C8×D6111yescharacteristic
741C2#418×D6111yescharacteristic
742C2#421×D6111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC4×C61C23×C8
FrattiniC42C23×D61
FittingC61×#1478C2
socleC22×C61C22×C22⋊C4
prime radicalC22×D4×D61C4
cosocleC42×C61C24
hypercenter#1478D61
hypocenterC61C2×#1478
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1478

Complements

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

NH ≅ G/Ntype
2. #431×D61C2semidirect
3. #431×D61C2semidirect
4. #21444211C2semidirect
5. #21444210C2semidirect
6. #21444209C2semidirect
7. #21444208C2semidirect
8. D4⋊C8×D61C2semidirect
9. C61×#1478C2semidirect
28. #16839815C22semidirect
29. #16839815C22semidirect
31. #16839814C22semidirect
33. #16839813C22semidirect
37. C4⋊C8×D61C22semidirect
41. C4×C8×D61C22semidirect
42. #16839491C22semidirect
43. D4⋊#92418C22semidirect
44. #16839489C22semidirect
46. C61×#431C22semidirect
47. C61×#431C22semidirect
48. C61×D4⋊C8C22semidirect
55. C2×D4×D61C8semidirect
117. C4⋊#92418C23semidirect
125. C4×#92418C23semidirect
138. C4⋊C8×C61C23semidirect
142. C4×C8×C61C23semidirect
153. C2×D4×C61C2×C8semidirect
177. D4×D61C2×C8semidirect
180. C2×D244C2×C8semidirect
371. #1478D61direct (N × H)
380. D61#1478direct (N × H)
408. #431C2×D61semidirect
409. #431C2×D61semidirect
419. D4⋊C8C2×D61semidirect
420. C61C2×#1478semidirect
502. C4⋊C8C22×D61semidirect
514. C4×C8C22×D61semidirect
538. C2×D4C8×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
#431×D612
#214442112
#214442102
#214442092
#214442082
D4⋊C8×D612
C61×#14782
C2×#147861