Finite Group Databasebeta

← #29685652

Subgroups — #29685652

Order 15616.

1952 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D61C211yesmaximal, characteristic, complemented
2C2×#16839894C211yesmaximal, characteristic
3C2×#16839872C211yesmaximal, characteristic, complemented
4C4×#14519748C211yesmaximal, characteristic, complemented
5#21446169C211yesmaximal, characteristic, complemented
6#21446164C211yesmaximal, characteristic, complemented
7#21446133C211yesmaximal, characteristic, complemented
8#21446078C211yesmaximal, characteristic, complemented
9#21446077C211yesmaximal, characteristic, complemented
10#21446010C211yesmaximal, characteristic, complemented
11#21445748C211yesmaximal, characteristic, complemented
12#21445645C211yesmaximal, characteristic, complemented
13#21445644C211yesmaximal, characteristic, complemented
14#21445582C211yesmaximal, characteristic, complemented
15C2×C61×#442C211yesmaximal, characteristic, complemented
16C22×D4×D61C2211yescharacteristic
17C23×C4×D61—21no—
18C22×#11758199C2211yescharacteristic
19C2×#14519748C2211yescharacteristic
20C2×C4×D244C2211yescharacteristic
21C2×D4×Dic61C2211yescharacteristic
22C2×#14519739C2211yescharacteristic
23C2×C4×C22⋊D61—21no—
24C2×C4×C22⋊D61—21no—
25C2×#14519737—21no—
26C4×D4×D61—24no—
27C4×D4×D61—24no—
28C2×C4⋊C4×D61C2211yescharacteristic
29C2×C22⋊C4×D61—21no—
30C2×C42×D61C2211yescharacteristic
31#16839894C418yescomplemented
32#16839872—24no—
33C2×#14519708C2211yescharacteristic, complemented
34C2×#14519699C2211yescharacteristic
35C2×#14519699C2211yescharacteristic
36C2×#14519698C2211yescharacteristic
37C2×#14519698C2211yescharacteristic
38C2×#14519698C2211yescharacteristic, complemented
39C2×#14519697C2211yescharacteristic
40C2×#14519689C2211yescharacteristic
41C2×#14519689C2211yescharacteristic
42C2×#14519688C2211yescharacteristic, complemented
43#16839665C2211yescharacteristic, complemented
44#16839658C2211yescharacteristic, complemented
45#16839650—21no—
46#16839638—21no—
47#16839619C2211yescharacteristic
48C4×C4⋊Dic61C2211yescharacteristic, complemented
49C4×C22⋊Dic61—21no—
50#16839525C2211yescharacteristic, complemented
51#16839525C2211yescharacteristic, complemented
52#16839524C2211yescharacteristic, complemented
53#16839524C2211yescharacteristic, complemented
54#16839516C2211yescharacteristic, complemented
55#16839516C2211yescharacteristic, complemented
56C22×D8×C61C2211yescharacteristic
57C2×C4×D4×C61C2211yescharacteristic
58C2×C4×D4×C61C2211yescharacteristic, complemented
59C61×#442—24no—
60C2×#106×C61C2211yescharacteristic, complemented
61C2×#102×C61C2211yescharacteristic
62C2×#102×C61C2211yescharacteristic, complemented
63C2×#97×C61C2211yescharacteristic, complemented
64C24×D61—21no—
65C22×D244C2311yescharacteristic
66C22×C22⋊D61—21no—
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×C414yescomplemented
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×#11758199—22no—
85C2×#11758199—22no—
86C2×#11758199C2×C414yescomplemented
87C22×#92418C2311yescharacteristic
88C22×#92418C2311yescharacteristic
89#14519748—22no—
90#14519748C2×C414yescomplemented
91C4×D244—22no—
92C4×D244D414yescomplemented
93D4×Dic61—22no—
94D4×Dic61—22no—
95#14519739—22no—
96#14519739—22no—
97C4×C22⋊D61—28no—
98C4×C22⋊D61—44no—
99#14519737—28no—
100C2×C4⋊Dic61C2311yescharacteristic
101C2×C4⋊Dic61C2311yescharacteristic
102C2×C4⋊Dic61C2311yescharacteristic
103C2×#11758196—21no—
104C2×#11758196—21no—
105C4⋊C4×D61—22no—
106C4⋊C4×D61—22no—
107C2×C22⋊Dic61—21no—
108C2×C22⋊Dic61—21no—
109C2×C22⋊Dic61—21no—
110C2×C22⋊Dic61—21no—
111C2×#11758198—21no—
112C2×#11758198—21no—
113C2×#11758198—21no—
114C22⋊C4×D61—28no—
115C2×C4×Dic61—21no—
116C2×C4×Dic61D411yescharacteristic
117C2×C4×Dic61D411yescharacteristic
118C2×C4×Dic61C2311yescharacteristic
119C42×D61—22no—
120C42×D61—22no—
121#14519708—22no—
122#14519699—22no—
123#14519699C2×C414yescomplemented
124#14519698—22no—
125#14519698—22no—
126#14519698C2×C414yescomplemented
127#14519697—22no—
128#14519689—22no—
129#14519689C2×C414yescomplemented
130#14519688—22no—
131#14519684—21no—
132#14519684—21no—
133#14519684—21no—
134C22×D4×C61C2311yescharacteristic
135C22×D4×C61C2311yescharacteristic
136C23×C4×C61—21no—
137C23×C4×C61—21no—
138C2×D8×C61—22no—
139C2×D8×C61—22no—
140C2×D8×C61C2×C414yescomplemented
141C22×C8×C61C2311yescharacteristic
142C22×C8×C61C2311yescharacteristic
143C4×D4×C61—22no—
144C4×D4×C61—22no—
145C4×D4×C61—22no—
146C4×D4×C61D414yescomplemented
147C2×C4⋊C4×C61C2311yescharacteristic
148C2×C4⋊C4×C61C2311yescharacteristic
149C2×C22⋊C4×C61—21no—
150C2×C22⋊C4×C61—21no—
151C2×C42×C61C2311yescharacteristic
152#106×C61—22no—
153#102×C61—22no—
154#102×C61—22no—
155#97×C61—22no—
156C24×C61—21no—
157C24×C61—21no—
158C23×D61—24no—
159C23×D61—24no—
160C23×D61—21no—
161C23×D61—24no—
162C23×D61—42no—
163C23×D61—42no—
164C23×D61—42no—
165C23×D61—42no—
166C23×D61C2×D411yescharacteristic
167C2×D4×C61—21no—
168C2×D4×C61—21no—
169C2×D4×C61—21no—
170C2×D4×C61—21no—
171C2×D4×C61—21no—
172C2×D4×C61—21no—
173C2×D4×C61—21no—
174C2×D4×C61—21no—
175C2×D4×C61C22×C412yes—
176C2×D4×C61C22×C412yescomplemented
177C2×D4×C61C2×D412yes—
178C2×D4×C61#4112yes—
179C22×C4×C61—21no—
180C22×C4×C61—24no—
181C22×C4×C61—21no—
182C22×C4×C61—42no—
183C22×C4×C61—42no—
184C22×C4×C61—42no—
185C22×C4×C61—42no—
186C22×C4×C61—42no—
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61C2×D411yescharacteristic
189C22×C4×C61C2411yescharacteristic
190C2×C22⋊D61—24no—
191C2×C22⋊D61—24no—
192C2×C22⋊D61—24no—
193C2×C22⋊D61—24no—
194C2×C22⋊D61—42no—
195C2×C22⋊D61—42no—
196C22×Dic61—24no—
197C22×Dic61—21no—
198C22×Dic61—21no—
199C22×Dic61—21no—
200C22×Dic61—42no—
201C22×Dic61—42no—
202C22×Dic61C2×D411yescharacteristic
203C22×Dic61C2×D411yescharacteristic
204C22×Dic61C2×D411yescharacteristic
205D4×D61—28no—
206D4×D61—28no—
207D4×D61—28no—
208D4×D61—28no—
209C2×D244—21no—
210C2×D244—21no—
211C2×D244—21no—
212C2×D244C22×C412yes—
213C2×D244C2×D412yes—
214C2×D244#4112yes—
215C2×C4×D61—22no—
216C2×C4×D61—22no—
217C2×C4×D61—21no—
218C2×C4×D61—21no—
219C2×C4×D61—21no—
220C2×C4×D61—21no—
221C2×C4×D61—22no—
222C2×C4×D61—24no—
223C2×C4×D61—24no—
224C2×C4×D61—22no—
225C2×C4×D61—24no—
226C2×C4×D61—22no—
227C2×C4×D61—432no—
228C2×C4×D61—41no—
229C2×C4×D61—42no—
230C2×C4×D61—42no—
231C2×C4×D61—42no—
232C2×C4×D61—42no—
233C2×C4×D61—42no—
234C2×C4×D61—42no—
235C2×C4×D61C22×C412yes—
236C2×C4×D61#4112yes—
237D8×C61—28no—
238C2×C8×C61—21no—
239C2×C8×C61—21no—
240C2×C8×C61—21no—
241C2×C8×C61—21no—
242C2×C8×C61—21no—
243C2×C8×C61C22×C412yescomplemented
244C4⋊C4×C61—21no—
245C4⋊C4×C61—21no—
246C4⋊C4×C61—21no—
247C4⋊C4×C61C2×D412yes—
248C22⋊C4×C61—24no—
249C22⋊C4×C61—42no—
250C42×C61C2×D412yes—
251C42×C61C2×D412yes—
252C22⋊Dic61—24no—
253C22⋊Dic61—24no—
254C22⋊Dic61—42no—
255C22⋊Dic61—42no—
256#11758199—28no—
257#11758198—24no—
258#11758198—24no—
259#11758198—42no—
260C4⋊Dic61—21no—
261C4⋊Dic61—21no—
262C4⋊Dic61—21no—
263C4⋊Dic61—21no—
264C4⋊Dic61C22×C412yescomplemented
265C4⋊Dic61C2×D412yes—
266#11758196—24no—
267#11758196—42no—
268C4×Dic61—22no—
269C4×Dic61—22no—
270C4×Dic61—21no—
271C4×Dic61—21no—
272C4×Dic61—42no—
273C2×#92418—21no—
274C2×#92418—21no—
275C2×#92418—21no—
276C2×#92418—21no—
277C2×#92418—21no—
278C2×#92418C22×C412yescomplemented
279C23×C61—22no—
280C23×C61—22no—
281C23×C61—22no—
282C23×C61—22no—
283C23×C61—41no—
284C23×C61—41no—
285C23×C61—41no—
286C23×C61—41no—
287C23×C61—41no—
288C23×C61—41no—
289C23×C61—41no—
290C23×C61—41no—
291C23×C61—41no—
292C23×C61—41no—
293C23×C61C22×D411yescharacteristic
294C22×D61—21no—
295C22×D61—21no—
296C22×D61—21no—
297C22×D61—21no—
298C22×D61—216no—
299C22×D61—22no—
300C22×D61—22no—
301C22×D61—22no—
302C22×D61—48no—
303C22×D61—48no—
304C22×D61—48no—
305C22×D61—48no—
306C22×D61—48no—
307C22×D61—41no—
308C22×D61—41no—
309C22×D61—41no—
310C22×D61—41no—
311C22×D61—48no—
312C22×D61C4×D412yes—
313C22×D61AGL(1,ℤ/8)12yes—
314C22×D61AGL(1,ℤ/8)12yes—
315D4×C61—22no—
316D4×C61—22no—
317D4×C61—22no—
318D4×C61—22no—
319D4×C61—22no—
320D4×C61—41no—
321D4×C61—41no—
322D4×C61C4×D414yescomplemented
323C2×C4×C61—21no—
324C2×C4×C61—21no—
325C2×C4×C61—21no—
326C2×C4×C61—21no—
327C2×C4×C61—22no—
328C2×C4×C61—48no—
329C2×C4×C61—41no—
330C2×C4×C61—41no—
331C2×C4×C61—41no—
332C2×C4×C61—41no—
333C2×C4×C61—41no—
334C2×C4×C61—84no—
335C2×C4×C61#12012yes—
336C2×C4×C61#12012yes—
337C2×C4×C61C23×C411yescharacteristic
338C2×C4×C61C22×D411yescharacteristic
339C2×C4×C61C22×D411yescharacteristic
340C2×C4×C61C2×#4111yescharacteristic
341C2×C4×C61C2×#4111yescharacteristic
342C2×C4×C61C2×#4111yescharacteristic
343C22⋊D61—216no—
344C22⋊D61—48no—
345C2×Dic61—21no—
346C2×Dic61—21no—
347C2×Dic61—21no—
348C2×Dic61—21no—
349C2×Dic61—22no—
350C2×Dic61—21no—
351C2×Dic61—22no—
352C2×Dic61—21no—
353C2×Dic61—21no—
354C2×Dic61—48no—
355C2×Dic61—41no—
356C2×Dic61—41no—
357C2×Dic61—41no—
358C2×Dic61—41no—
359C2×Dic61—41no—
360C2×Dic61—41no—
361C2×Dic61—41no—
362C2×Dic61C4×D412yes—
363C2×Dic61AGL(1,ℤ/8)12yes—
364D244—22no—
365D244—22no—
366D244—22no—
367D244C4×D414yescomplemented
368C4×D61—28no—
369C4×D61—22no—
370C4×D61—22no—
371C4×D61—22no—
372C4×D61—22no—
373C4×D61—48no—
374C4×D61—44no—
375C4×D61—48no—
376C4×D61—48no—
377C8×C61—22no—
378C8×C61—41no—
379#92418—22no—
380#92418—41no—
381#21452—611nomaximal, Sylow
382C22×C61—24no—
383C22×C61—42no—
384C22×C61—42no—
385C22×C61—42no—
386C22×C61—42no—
387C22×C61—42no—
388C22×C61—42no—
389C22×C61—42no—
390C22×C61—42no—
391C22×C61—42no—
392C22×C61—81no—
393C22×C61—81no—
394C22×C61—81no—
395C22×C61—81no—
396C22×C61C2×C4×D411yescharacteristic
397C22×C61C2×#12011yescharacteristic
398C22×C61#52511yescharacteristic
399C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
400C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
401C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
402C22×C61#57511yescharacteristic
403C2×D61—22no—
404C2×D61—22no—
405C2×D61—22no—
406C2×D61—22no—
407C2×D61—22no—
408C2×D61—22no—
409C2×D61—24no—
410C2×D61—432no—
411C2×D61—42no—
412C2×D61—42no—
413C2×D61—42no—
414C2×D61—42no—
415C2×D61—42no—
416C2×D61—42no—
417C2×D61#44214yescomplemented
418C4×C61—22no—
419C4×C61—22no—
420C4×C61—42no—
421C4×C61—81no—
422C4×C61C2×C4×D411yescharacteristic
423C4×C61C2×C4×D411yescharacteristic
424C4×C61#52511yescharacteristic
425C4×C61#52511yescharacteristic
426Dic61—22no—
427Dic61—22no—
428Dic61—42no—
429Dic61—42no—
430Dic61—41no—
431Dic61—81no—
432C22×C4×D4—611no—
433C2×#447—611no—
434C2×#442—611no—
435C2×#442D6111yescharacteristic, complemented
436C4×#121—611no—
437#1879—611no—
438#1879—611no—
439#1874—611no—
440#1864—611no—
441#1864—611no—
442#1853—611no—
443#1786—611no—
444#1762—611no—
445#1762—611no—
446#1749—611no—
447C2×C61—44no—
448C2×C61—82no—
449C2×C61C4×#12011yescharacteristic
450C2×C61C2×#44211yescharacteristic
451C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
452C2×C61#300311yescharacteristic
453C2×C61#300611yescharacteristic
454C2×C61#310911yescharacteristic
455C2×C61#311411yescharacteristic
456D61—24no—
457D61—44no—
458C23×D4—611no—
459C24×C4—1221no—
460C22×D8—611no—
461C22×D8C2×D6111yescharacteristic
462C2×#121—611no—
463C2×C4×D4—611no—
464C2×C4×D4—611no—
465C2×C4×D4—611no—
466C2×C4×D4—1221no—
467C2×C4×D4—1221no—
468C2×C4×D4—1224no—
469C2×C4×D4—1224no—
470C2×C4×D4—1221no—
471C2×C4×D4C2×D6111yescharacteristic
472C2×C4×D4C2×D6111yescharacteristic, complemented
473C22×C4⋊C4—611no—
474C22×C22⋊C4—1221no—
475C22×C42—611no—
476#447—618no—
477#442—24no—
478#442—1224no—
479C2×#106—611no—
480C2×#106C2×D6111yescharacteristic, complemented
481C2×#102—611no—
482C2×#102—611no—
483C2×#102—611no—
484C2×#102—611no—
485C2×#102—611no—
486C2×#102—611no—
487C2×#102C2×D6111yescharacteristic
488C2×#102C2×D6111yescharacteristic, complemented
489C2×C22⋊C8—611no—
490C2×C22⋊C8—611no—
491C2×#97—611no—
492C2×#97C2×D6111yescharacteristic, complemented
493#390—611no—
494#389—611no—
495#388—1221no—
496#386—1221no—
497#380—611no—
498C4×C4⋊C4—611no—
499C4×C22⋊C4—1221no—
500#340—611no—
501#340—611no—
502#340—611no—
503#340—611no—
504#336—611no—
505#336—611no—
506C61#2145211yescharacteristic, complemented, Sylow
507C25—1221no—
508C22×D4—614no—
509C22×D4—611no—
510C22×D4—1222no—
511C22×D4—1221no—
512C22×D4—1222no—
513C22×D4—1222no—
514C22×D4—1222no—
515C22×D4—1222no—
516C22×D4—1221no—
517C22×D4C22×D6111yescharacteristic
518C22×D4C22×D6111yescharacteristic
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—611no—
522C23×C4—611no—
523C23×C4—611no—
524C23×C4—1221no—
525C23×C4—1221no—
526C23×C4—1228no—
527C23×C4—1221no—
528C23×C4—1221no—
529C23×C4—2444no—
530C23×C4—2444no—
531C2×D8—22no—
532C2×D8—22no—
533C2×D8—614no—
534C2×D8—1222no—
535C2×D8—1222no—
536C2×D8C4×D6114yescomplemented
537C22×C8—611no—
538C22×C8—611no—
539C22×C8C22×D6111yescharacteristic
540C22×C8C22×D6111yescharacteristic
541#121—614no—
542#121—1222no—
543C4×D4—22no—
544C4×D4—22no—
545C4×D4—22no—
546C4×D4—614no—
547C4×D4—1228no—
548C4×D4—1222no—
549C4×D4—1222no—
550C4×D4—1228no—
551C4×D4—1222no—
552C4×D4—1222no—
553C4×D4—1222no—
554C4×D4—2444no—
555C4×D4C22⋊D6114yescomplemented
556C2×C4⋊C4—611no—
557C2×C4⋊C4—611no—
558C2×C4⋊C4—611no—
559C2×C4⋊C4—1222no—
560C2×C4⋊C4—1221no—
561C2×C4⋊C4—1222no—
562C2×C4⋊C4—1221no—
563C2×C4⋊C4C22×D6111yescharacteristic
564C2×C4⋊C4C22×D6111yescharacteristic
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—1228no—
568C2×C22⋊C4—1221no—
569C2×C22⋊C4—1221no—
570C2×C22⋊C4—1221no—
571C2×C22⋊C4—1221no—
572C2×C22⋊C4—1221no—
573C2×C22⋊C4—1221no—
574C2×C22⋊C4—1221no—
575C2×C42—611no—
576C2×C42—611no—
577C2×C42—611no—
578C2×C42—1222no—
579C2×C42—1222no—
580C2×C42—1221no—
581C2×C42C22×D6111yescharacteristic
582#106—22no—
583#106—1222no—
584#102—22no—
585#102—22no—
586#102—614no—
587#102—614no—
588#102—1222no—
589#102—1222no—
590#102—1222no—
591#102—1222no—
592C22⋊C8—614no—
593C22⋊C8—1222no—
594#97—22no—
595#97—1222no—
596#95—1221no—
597#95—1221no—
598#95—1221no—
599C24—21no—
600C24—21no—
601C24—611no—
602C24—1224no—
603C24—1224no—
604C24—1224no—
605C24—1221no—
606C24—2442no—
607C24—2442no—
608C24—2442no—
609C24—2442no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—612no—
619C2×D4—612no—
620C2×D4—612no—
621C2×D4—1224no—
622C2×D4—1228no—
623C2×D4—1228no—
624C2×D4—1228no—
625C2×D4—1224no—
626C2×D4—1224no—
627C2×D4—1228no—
628C2×D4—1224no—
629C2×D4—1221no—
630C2×D4—1221no—
631C2×D4—1221no—
632C2×D4—2442no—
633C2×D4—2442no—
634C2×D4C2×C4×D6112yes—
635C2×D4C2×C4×D6112yescomplemented
636C2×D4#1175822212yes—
637C2×D4C2×C22⋊D6112yes—
638C22×C4—21no—
639C22×C4—24no—
640C22×C4—21no—
641C22×C4—42no—
642C22×C4—42no—
643C22×C4—42no—
644C22×C4—42no—
645C22×C4—42no—
646C22×C4—611no—
647C22×C4—611no—
648C22×C4—612no—
649C22×C4—612no—
650C22×C4—611no—
651C22×C4—1222no—
652C22×C4—1222no—
653C22×C4—1222no—
654C22×C4—1224no—
655C22×C4—1224no—
656C22×C4—1221no—
657C22×C4—1221no—
658C22×C4—1221no—
659C22×C4—1221no—
660C22×C4—1222no—
661C22×C4—1224no—
662C22×C4—1221no—
663C22×C4—1221no—
664C22×C4—1222no—
665C22×C4—1224no—
666C22×C4—1221no—
667C22×C4—2441no—
668C22×C4—2442no—
669C22×C4—2442no—
670C22×C4—2442no—
671C22×C4—24432no—
672C22×C4—2442no—
673C22×C4—2442no—
674C22×C4—2442no—
675C22×C4—2442no—
676C22×C4—2442no—
677C22×C4D4×D6111yescharacteristic
678C22×C4D4×D6111yescharacteristic
679C22×C4C23×D6111yescharacteristic
680D8—28no—
681D8—1228no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—612no—
688C2×C8—1221no—
689C2×C8—1221no—
690C2×C8—1221no—
691C2×C8—1221no—
692C2×C8—1221no—
693C2×C8C2×C4×D6112yescomplemented
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—612no—
698C4⋊C4—612no—
699C4⋊C4—1224no—
700C4⋊C4—1221no—
701C4⋊C4—1221no—
702C4⋊C4—1221no—
703C4⋊C4—1221no—
704C4⋊C4—2442no—
705C4⋊C4C2×C22⋊D6112yes—
706C22⋊C4—24no—
707C22⋊C4—42no—
708C22⋊C4—1224no—
709C22⋊C4—1224no—
710C22⋊C4—1224no—
711C22⋊C4—1224no—
712C22⋊C4—2442no—
713C22⋊C4—2442no—
714C22⋊C4—2442no—
715C42—1221no—
716C42—1221no—
717C42—1222no—
718C42—1222no—
719C42—2442no—
720C42D4×D6112yes—
721C42C2×C22⋊D6112yes—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—612no—
737C23—612no—
738C23—612no—
739C23—12216no—
740C23—1221no—
741C23—1221no—
742C23—1221no—
743C23—1221no—
744C23—1222no—
745C23—1222no—
746C23—1222no—
747C23—2448no—
748C23—2448no—
749C23—2448no—
750C23—2448no—
751C23—2448no—
752C23—2448no—
753C23—2441no—
754C23—2441no—
755C23—2441no—
756C23—2441no—
757C23C2×D4×D6111yescharacteristic
758D4—22no—
759D4—22no—
760D4—22no—
761D4—22no—
762D4—22no—
763D4—41no—
764D4—41no—
765D4—614no—
766D4—12216no—
767D4—1222no—
768D4—1222no—
769D4—1222no—
770D4—2448no—
771D4C4×C22⋊D6114yescomplemented
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—48no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—84no—
784C2×C4—612no—
785C2×C4—612no—
786C2×C4—1228no—
787C2×C4—1221no—
788C2×C4—1221no—
789C2×C4—1221no—
790C2×C4—1221no—
791C2×C4—1222no—
792C2×C4—1222no—
793C2×C4—1222no—
794C2×C4—1222no—
795C2×C4—1222no—
796C2×C4—1221no—
797C2×C4—1222no—
798C2×C4—1221no—
799C2×C4—1221no—
800C2×C4—2444no—
801C2×C4—2448no—
802C2×C4—2448no—
803C2×C4—2448no—
804C2×C4—2448no—
805C2×C4—2441no—
806C2×C4—2441no—
807C2×C4—2441no—
808C2×C4—2441no—
809C2×C4—2441no—
810C2×C4—2441no—
811C2×C4—2441no—
812C2×C4#1451974512yes—
813C2×C4#1451974512yes—
814C2×C4C22×C4×D6111yescharacteristic
815C2×C4C2×D4×D6111yescharacteristic
816C2×C4C22×C22⋊D6111yescharacteristic
817C2×C4#41×D6111yescharacteristic
818C2×C4#41×D6111yescharacteristic
819C2×C4C2×#1175822211yescharacteristic
820C8—22no—
821C8—41no—
822C8—1222no—
823C8—2441no—
824C22—24no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—81no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—614no—
839C22—1222no—
840C22—1222no—
841C22—1222no—
842C22—1222no—
843C22—1222no—
844C22—1222no—
845C22—1224no—
846C22—24432no—
847C22—2442no—
848C22—2442no—
849C22—2442no—
850C22—2442no—
851C22—2442no—
852C22—2442no—
853C22C4×D4×D6111yescharacteristic
854C22C2×#1451974511yescharacteristic
855C22#1684027111yescharacteristic
856C22AGL(1,ℤ/8)×D6111yescharacteristic
857C22AGL(1,ℤ/8)×D6111yescharacteristic
858C22AGL(1,ℤ/8)×D6111yescharacteristic
859C22#1684055811yescharacteristic
860C4—22no—
861C4—22no—
862C4—42no—
863C4—81no—
864C4—1222no—
865C4—1222no—
866C4—4881no—
867C4—2442no—
868C4—2442no—
869C4—2441no—
870C4C4×D4×D6111yescharacteristic
871C4C2×C4×C22⋊D6111yescharacteristic
872C4#1684026911yescharacteristic
873C4#1684027111yescharacteristic
874C2—44no—
875C2—82no—
876C2—1224no—
877C2—2444no—
878C2C4×#1451974511yescharacteristic
879C2#442×D6111yescharacteristic
880C2#2145463011yescharacteristic
881C2#2145504411yescharacteristic
882C2#2145506711yescharacteristic
883C2#2145590811yescharacteristic
884C2#2145595511yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#442C2
socleC23×C61C22×D4
prime radicalC2×#16839894C2
cosocleC22×C4×C61C24
hypercenterC2×#442D61
hypocenterC61#21452
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
1. C2×C4×D4×D61C2semidirect
3. C2×#16839872C2semidirect
4. C4×#14519748C2semidirect
5. #21446169C2semidirect
6. #21446164C2semidirect
7. #21446133C2semidirect
8. #21446078C2semidirect
9. #21446077C2semidirect
10. #21446010C2semidirect
11. #21445748C2semidirect
12. #21445645C2semidirect
13. #21445644C2semidirect
14. #21445582C2semidirect
15. C2×C61×#442C2semidirect
31. #16839894C4semidirect
33. C2×#14519708C22semidirect
38. C2×#14519698C22semidirect
42. C2×#14519688C22semidirect
43. #16839665C22semidirect
44. #16839658C22semidirect
48. C4×C4⋊Dic61C22semidirect
50. #16839525C22semidirect
51. #16839525C22semidirect
52. #16839524C22semidirect
53. #16839524C22semidirect
54. #16839516C22semidirect
55. #16839516C22semidirect
58. C2×C4×D4×C61C22semidirect
60. C2×#106×C61C22semidirect
62. C2×#102×C61C22semidirect
63. C2×#97×C61C22semidirect
73. C2×D4×D61C2×C4semidirect
86. C2×#11758199C2×C4semidirect
90. #14519748C2×C4semidirect
92. C4×D244D4semidirect
123. #14519699C2×C4semidirect
126. #14519698C2×C4semidirect
129. #14519689C2×C4semidirect
140. C2×D8×C61C2×C4semidirect
146. C4×D4×C61D4semidirect
176. C2×D4×C61C22×C4semidirect
243. C2×C8×C61C22×C4semidirect
264. C4⋊Dic61C22×C4semidirect
278. C2×#92418C22×C4semidirect
322. D4×C61C4×D4semidirect
367. D244C4×D4semidirect
417. C2×D61#442semidirect
435. C2×#442D61semidirect
472. C2×C4×D4C2×D61semidirect
480. C2×#106C2×D61semidirect
488. C2×#102C2×D61semidirect
492. C2×#97C2×D61semidirect
506. C61#21452semidirect
536. C2×D8C4×D61semidirect
555. C4×D4C22⋊D61semidirect
635. C2×D4C2×C4×D61semidirect
693. C2×C8C2×C4×D61semidirect
771. D4C4×C22⋊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×#168398942
C2×#168398722
C4×#145197482
#214461692
#214461642
#214461332
#214460782
#214460772
#214460102
#214457482
#214456452
#214456442
#214455822
C2×C61×#4422
#2145261