Finite Group Databasebeta

← #29695553

Subgroups — #29695553

Order 15616.

1930 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839834C211yesmaximal, characteristic, complemented
2C2×#16839767C211yesmaximal, characteristic, complemented
3C22×#14519698C211yesmaximal, characteristic, complemented
4#21448748C211yesmaximal, characteristic, complemented
5#21446747C211yesmaximal, characteristic, complemented
6#21446644C211yesmaximal, characteristic, complemented
7#21446258C211yesmaximal, characteristic, complemented
8#21446248C211yesmaximal, characteristic, complemented
9#21446142C211yesmaximal, characteristic, complemented
10#21446137C211yesmaximal, characteristic, complemented
11#21445829C211yesmaximal, characteristic, complemented
12#21445750C211yesmaximal, characteristic, complemented
13#21445750C211yesmaximal, characteristic, complemented
14#21445644C211yesmaximal, characteristic, complemented
15C2×D42×C61C211yesmaximal, characteristic
16C22×#11758194C2211yescharacteristic, complemented
17C23×#92418C2211yescharacteristic, complemented
18C2×#14519736C2211yescharacteristic, complemented
19C22×C4⋊Dic61C2211yescharacteristic, complemented
20#16839834—24no—
21C2×C4⋊#92418C2211yescharacteristic, complemented
22#16839767—24no—
23C2×#14519698—24no—
24C2×#14519698C2211yescharacteristic
25C2×#14519698C2211yescharacteristic
26C2×#14519698C2211yescharacteristic
27C2×#14519698C2211yescharacteristic
28C2×#14519698C2211yescharacteristic, complemented
29C2×#14519698C2211yescharacteristic, complemented
30C2×#14519698C2211yescharacteristic, complemented
31C2×#14519698C2211yescharacteristic, complemented
32C2×#14519698C2211yescharacteristic, complemented
33C2×#14519698C2211yescharacteristic, complemented
34C2×#14519698C2211yescharacteristic, complemented
35C2×#14519698C2211yescharacteristic, complemented
36C2×C22⋊#92418C2211yescharacteristic, complemented
37C2×C22⋊#92418C2211yescharacteristic, complemented
38C2×#14519688C2211yescharacteristic, complemented
39#16839655—21no—
40#16839648—21no—
41#16839642—21no—
42#16839628C2211yescharacteristic, complemented
43#16839622C2211yescharacteristic, complemented
44#16839622C2211yescharacteristic, complemented
45C4×C4⋊Dic61C2211yescharacteristic, complemented
46C22⋊C4×Dic61—21no—
47#16839524C2211yescharacteristic, complemented
48#16839524C2211yescharacteristic, complemented
49#16839524C2211yescharacteristic, complemented
50#16839524C2211yescharacteristic, complemented
51C23×D4×C61—21no—
52C23×D4×C61C2211yescharacteristic
53C23×D4×C61C2211yescharacteristic
54D42×C61—24no—
55D42×C61C418yescomplemented
56C2×#127×C61C2211yescharacteristic
57C2×#121×C61—21no—
58C2×#121×C61C2211yescharacteristic
59C2×#121×C61C2211yescharacteristic
60C2×#120×C61—21no—
61C2×#120×C61—21no—
62C2×C4×D4×C61C2211yescharacteristic
63C2×C4×D4×C61C2211yescharacteristic
64C23×Dic61—21no—
65C2×#11758194—22no—
66C2×#11758194—22no—
67C2×#11758194—41no—
68C22×#92418—22no—
69C22×#92418—22no—
70C22×#92418—41no—
71C22×#92418C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74C22×#92418C2311yescharacteristic
75#14519736—22no—
76#14519736—41no—
77C2×C4⋊Dic61—22no—
78C2×C4⋊Dic61—21no—
79C2×C4⋊Dic61—41no—
80C2×C4⋊Dic61C2311yescharacteristic
81C2×C4⋊Dic61C2311yescharacteristic
82C2×C4⋊Dic61C2311yescharacteristic
83C2×C4⋊Dic61C2311yescharacteristic
84C2×C22⋊Dic61—21no—
85C2×C22⋊Dic61—21no—
86C2×C22⋊Dic61—21no—
87C2×C4×Dic61—21no—
88C2×C4×Dic61—21no—
89C4⋊#92418—22no—
90#14519698—22no—
91#14519698—22no—
92#14519698—22no—
93#14519698—22no—
94#14519698—22no—
95#14519698—22no—
96#14519698—22no—
97#14519698—41no—
98#14519698—41no—
99#14519698—41no—
100#14519698—41no—
101#14519698D414yescomplemented
102C22⋊#92418—22no—
103C22⋊#92418—22no—
104#14519688—22no—
105#14519684—21no—
106#14519684—21no—
107#14519684—21no—
108#14519684—21no—
109#14519684—21no—
110C25×C61—21no—
111C25×C61—21no—
112C22×D4×C61—22no—
113C22×D4×C61—22no—
114C22×D4×C61—22no—
115C22×D4×C61—22no—
116C22×D4×C61—21no—
117C22×D4×C61—21no—
118C22×D4×C61—28no—
119C22×D4×C61—21no—
120C22×D4×C61—22no—
121C22×D4×C61—22no—
122C22×D4×C61—21no—
123C22×D4×C61—21no—
124C22×D4×C61—21no—
125C22×D4×C61—41no—
126C22×D4×C61—41no—
127C22×D4×C61—41no—
128C22×D4×C61—41no—
129C22×D4×C61—44no—
130C22×D4×C61—44no—
131C22×D4×C61C2×C414yes—
132C22×D4×C61C2×C414yescomplemented
133C22×D4×C61D411yescharacteristic
134C22×D4×C61C2311yescharacteristic
135C22×D4×C61C2311yescharacteristic
136C22×D4×C61C2311yescharacteristic
137C23×C4×C61—21no—
138C23×C4×C61C2311yescharacteristic
139C23×C4×C61C2311yescharacteristic
140#127×C61—22no—
141#127×C61C2×C414yescomplemented
142#121×C61—22no—
143#121×C61—22no—
144#121×C61—28no—
145#121×C61C2×C414yes—
146#121×C61C2×C414yescomplemented
147#120×C61—28no—
148#120×C61—28no—
149C4×D4×C61—22no—
150C4×D4×C61C2×C414yes—
151C4×D4×C61C2×C414yescomplemented
152C4×D4×C61D414yes—
153C2×C4⋊C4×C61D411yescharacteristic
154C2×C4⋊C4×C61C2311yescharacteristic
155C2×C22⋊C4×C61—21no—
156C2×C22⋊C4×C61—21no—
157C2×C22⋊C4×C61—21no—
158C2×C22⋊C4×C61D411yescharacteristic
159C2×C22⋊C4×C61D411yescharacteristic
160C2×C42×C61C2311yescharacteristic
161C24×C61—21no—
162C24×C61—21no—
163C24×C61—21no—
164C24×C61—24no—
165C24×C61—24no—
166C24×C61—42no—
167C24×C61—42no—
168C24×C61—42no—
169C24×C61—42no—
170C24×C61—42no—
171C24×C61—42no—
172C24×C61—42no—
173C24×C61—42no—
174C24×C61—81no—
175C24×C61—81no—
176C24×C61—81no—
177C24×C61—81no—
178C24×C61C2×D411yescharacteristic
179C24×C61C2×D411yescharacteristic
180C2×D4×C61—22no—
181C2×D4×C61—22no—
182C2×D4×C61—28no—
183C2×D4×C61—28no—
184C2×D4×C61—24no—
185C2×D4×C61—24no—
186C2×D4×C61—24no—
187C2×D4×C61—24no—
188C2×D4×C61—24no—
189C2×D4×C61—24no—
190C2×D4×C61—21no—
191C2×D4×C61—21no—
192C2×D4×C61—21no—
193C2×D4×C61—21no—
194C2×D4×C61—21no—
195C2×D4×C61—21no—
196C2×D4×C61—21no—
197C2×D4×C61—21no—
198C2×D4×C61—21no—
199C2×D4×C61—21no—
200C2×D4×C61—21no—
201C2×D4×C61—21no—
202C2×D4×C61—21no—
203C2×D4×C61—44no—
204C2×D4×C61—44no—
205C2×D4×C61—44no—
206C2×D4×C61—44no—
207C2×D4×C61—44no—
208C2×D4×C61—44no—
209C2×D4×C61—42no—
210C2×D4×C61—42no—
211C2×D4×C61—42no—
212C2×D4×C61—42no—
213C2×D4×C61—42no—
214C2×D4×C61—42no—
215C2×D4×C61—432no—
216C2×D4×C61—42no—
217C2×D4×C61—42no—
218C2×D4×C61—42no—
219C2×D4×C61—42no—
220C2×D4×C61—81no—
221C2×D4×C61—81no—
222C2×D4×C61C22⋊C414yes—
223C2×D4×C61C22×C412yes—
224C2×D4×C61C22×C412yes—
225C2×D4×C61C22×C412yes—
226C2×D4×C61C2×D412yes—
227C2×D4×C61#4112yes—
228C22×C4×C61—21no—
229C22×C4×C61—21no—
230C22×C4×C61—21no—
231C22×C4×C61—21no—
232C22×C4×C61—21no—
233C22×C4×C61—21no—
234C22×C4×C61—21no—
235C22×C4×C61—21no—
236C22×C4×C61—21no—
237C22×C4×C61—24no—
238C22×C4×C61—42no—
239C22×C4×C61—42no—
240C22×C4×C61C22×C412yes—
241C22×C4×C61C22×C412yes—
242C22×C4×C61C2×D411yescharacteristic
243C22×C4×C61C2×D411yescharacteristic
244C22×C4×C61C2×D411yescharacteristic
245C22×C4×C61C2×D411yescharacteristic
246C22×C4×C61C2×D412yes—
247C22×C4×C61C2×D412yes—
248C22×C4×C61C2411yescharacteristic
249C22×Dic61—21no—
250C22×Dic61—21no—
251C22×Dic61—21no—
252C22×Dic61—21no—
253C22×Dic61—42no—
254C22×Dic61—42no—
255C22×Dic61—81no—
256C4⋊C4×C61—21no—
257C4⋊C4×C61C22⋊C414yes—
258C4⋊C4×C61C22×C412yes—
259C22⋊C4×C61—24no—
260C22⋊C4×C61—24no—
261C22⋊C4×C61—24no—
262C22⋊C4×C61C22⋊C414yes—
263C22⋊C4×C61C22⋊C414yes—
264C42×C61C22×C412yes—
265C42×C61C2×D412yes—
266C22⋊Dic61—42no—
267C22⋊Dic61—42no—
268C22⋊Dic61—81no—
269C4⋊Dic61—21no—
270C4⋊Dic61—21no—
271C4⋊Dic61—21no—
272C4⋊Dic61—21no—
273C4⋊Dic61—21no—
274C4⋊Dic61—21no—
275C4⋊Dic61—21no—
276C4⋊Dic61—42no—
277C4⋊Dic61C2×D412yescomplemented
278C4×Dic61—42no—
279C4×Dic61—81no—
280#11758194—44no—
281C2×#92418—21no—
282C2×#92418—21no—
283C2×#92418—21no—
284C2×#92418—21no—
285C2×#92418—21no—
286C2×#92418—21no—
287C2×#92418—21no—
288C2×#92418—21no—
289C2×#92418—21no—
290C2×#92418—21no—
291C2×#92418—21no—
292C2×#92418—44no—
293C2×#92418C2×D412yescomplemented
294C23×C61—21no—
295C23×C61—21no—
296C23×C61—21no—
297C23×C61—21no—
298C23×C61—22no—
299C23×C61—21no—
300C23×C61—22no—
301C23×C61—21no—
302C23×C61—22no—
303C23×C61—21no—
304C23×C61—21no—
305C23×C61—21no—
306C23×C61—21no—
307C23×C61—22no—
308C23×C61—22no—
309C23×C61—48no—
310C23×C61—48no—
311C23×C61—48no—
312C23×C61—41no—
313C23×C61—41no—
314C23×C61—41no—
315C23×C61—41no—
316C23×C61—41no—
317C23×C61—41no—
318C23×C61—41no—
319C23×C61—41no—
320C23×C61—41no—
321C23×C61—41no—
322C23×C61—41no—
323C23×C61—41no—
324C23×C61—41no—
325C23×C61—41no—
326C23×C61—41no—
327C23×C61—41no—
328C23×C61—48no—
329C23×C61—84no—
330C23×C61—84no—
331C23×C61—84no—
332C23×C61—84no—
333C23×C61—84no—
334C23×C61—84no—
335C23×C61—84no—
336C23×C61—84no—
337C23×C61—84no—
338C23×C61—84no—
339C23×C61C2×C22⋊C412yes—
340C23×C61C2×C22⋊C412yes—
341C23×C61AGL(1,ℤ/8)12yes—
342C23×C61AGL(1,ℤ/8)12yes—
343C23×C61C22×D411yescharacteristic
344D4×C61—28no—
345D4×C61—22no—
346D4×C61—22no—
347D4×C61—22no—
348D4×C61—22no—
349D4×C61—22no—
350D4×C61—22no—
351D4×C61—22no—
352D4×C61—48no—
353D4×C61—48no—
354D4×C61—48no—
355D4×C61—48no—
356D4×C61—48no—
357D4×C61—41no—
358D4×C61—41no—
359D4×C61—41no—
360D4×C61—41no—
361D4×C61—84no—
362D4×C61C4×D414yes—
363C2×C4×C61—21no—
364C2×C4×C61—21no—
365C2×C4×C61—21no—
366C2×C4×C61—21no—
367C2×C4×C61—21no—
368C2×C4×C61—21no—
369C2×C4×C61—21no—
370C2×C4×C61—21no—
371C2×C4×C61—22no—
372C2×C4×C61—22no—
373C2×C4×C61—22no—
374C2×C4×C61—22no—
375C2×C4×C61—22no—
376C2×C4×C61—22no—
377C2×C4×C61—22no—
378C2×C4×C61—22no—
379C2×C4×C61—22no—
380C2×C4×C61—48no—
381C2×C4×C61—41no—
382C2×C4×C61—41no—
383C2×C4×C61C2×C22⋊C412yes—
384C2×C4×C61C2×C22⋊C412yes—
385C2×C4×C61C2×C22⋊C412yes—
386C2×C4×C61C2×C22⋊C412yes—
387C2×C4×C61C23×C411yescharacteristic
388C2×C4×C61C22×D411yescharacteristic
389C2×C4×C61C22×D411yescharacteristic
390C2×C4×C61C2×#4111yescharacteristic
391C2×C4×C61H(5,𝔽2)11yescharacteristic
392C2×C4×C61H(5,𝔽2)11yescharacteristic
393C2×Dic61—22no—
394C2×Dic61—41no—
395C2×Dic61—41no—
396C2×Dic61—41no—
397C2×Dic61—41no—
398C2×Dic61—41no—
399C2×Dic61—41no—
400C2×Dic61—41no—
401C2×Dic61—41no—
402C2×Dic61—41no—
403C2×Dic61—41no—
404C2×Dic61—41no—
405C2×Dic61—84no—
406#92418—22no—
407#92418—41no—
408#92418—41no—
409#92418—41no—
410#22423—611nomaximal, Sylow
411C22×C61—22no—
412C22×C61—22no—
413C22×C61—22no—
414C22×C61—22no—
415C22×C61—22no—
416C22×C61—22no—
417C22×C61—22no—
418C22×C61—24no—
419C22×C61—22no—
420C22×C61—22no—
421C22×C61—42no—
422C22×C61—42no—
423C22×C61—41no—
424C22×C61—42no—
425C22×C61—41no—
426C22×C61—42no—
427C22×C61—41no—
428C22×C61—42no—
429C22×C61—41no—
430C22×C61—42no—
431C22×C61—42no—
432C22×C61—42no—
433C22×C61—42no—
434C22×C61—42no—
435C22×C61—42no—
436C22×C61—42no—
437C22×C61—816no—
438C22×C61—816no—
439C22×C61—81no—
440C22×C61—81no—
441C22×C61—81no—
442C22×C61—81no—
443C22×C61—81no—
444C22×C61—81no—
445C22×C61—81no—
446C22×C61—81no—
447C22×C61#41814yescomplemented
448C22×C61C22×C22⋊C411yescharacteristic
449C22×C61D4211yescharacteristic
450C22×C61#54611yescharacteristic
451C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
452C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
453C22×C61#57611yescharacteristic
454C22×C61#57711yescharacteristic
455C4×C61—22no—
456C4×C61—22no—
457C4×C61—22no—
458C4×C61—22no—
459C4×C61—42no—
460C4×C61C2×C4×D411yescharacteristic
461C4×C61#51811yescharacteristic
462C4×C61D4211yescharacteristic
463C4×C61#54611yescharacteristic
464Dic61—42no—
465Dic61—81no—
466Dic61—81no—
467Dic61—81no—
468C2×D42D6111yescharacteristic
469C2×#435—611no—
470C2×#418—611no—
471C22×#102—611no—
472#2352—611no—
473#1982—611no—
474#1961—611no—
475#1895—611no—
476#1893—611no—
477#1875—611no—
478#1874—611no—
479#1804—611no—
480#1786—611no—
481#1786—611no—
482#1762—611no—
483C2×C61—24no—
484C2×C61—42no—
485C2×C61—44no—
486C2×C61—82no—
487C2×C61—82no—
488C2×C61D4×C22⋊C411yescharacteristic
489C2×C61C2×#41811yescharacteristic
490C2×C61#289711yescharacteristic
491C2×C61#326411yescharacteristic
492C2×C61#326511yescharacteristic
493C2×C61#331011yescharacteristic
494C2×C61#331811yescharacteristic
495C23×D4—21no—
496C23×D4C2×D6111yescharacteristic
497C23×D4C2×D6111yescharacteristic
498C22×M16—611no—
499C23×C8—611no—
500D42—24no—
501D42Dic6118yescomplemented
502C2×#127C2×D6111yescharacteristic
503C2×#121—21no—
504C2×#121C2×D6111yescharacteristic
505C2×#121C2×D6111yescharacteristic
506C2×#120—21no—
507C2×#120—21no—
508C2×C4×D4C2×D6111yescharacteristic
509C2×C4×D4C2×D6111yescharacteristic
510C2×#117—611no—
511C22×C4⋊C4—611no—
512#435—1224no—
513C2×C4⋊C8—611no—
514#418—1224no—
515C2×#102—611no—
516C2×#102—611no—
517C2×#102—611no—
518C2×#102—611no—
519C2×#102—611no—
520C2×#102—611no—
521C2×#102—611no—
522C2×#102—611no—
523C2×#102—611no—
524C2×#102—611no—
525C2×#102—611no—
526C2×#102—611no—
527C2×#102—1224no—
528C2×C22⋊C8—611no—
529C2×C22⋊C8—611no—
530C2×#97—611no—
531#388—1221no—
532#387—1221no—
533#386—1221no—
534#382—611no—
535#380—611no—
536#380—611no—
537C4×C4⋊C4—611no—
538C4×C22⋊C4—1221no—
539#340—611no—
540#340—611no—
541#340—611no—
542#340—611no—
543C61#2242311yescharacteristic, complemented, Sylow
544C25—21no—
545C25—21no—
546C22×D4—22no—
547C22×D4—22no—
548C22×D4—22no—
549C22×D4—22no—
550C22×D4—21no—
551C22×D4—21no—
552C22×D4—28no—
553C22×D4—21no—
554C22×D4—21no—
555C22×D4—21no—
556C22×D4—22no—
557C22×D4—22no—
558C22×D4—21no—
559C22×D4—41no—
560C22×D4—41no—
561C22×D4—41no—
562C22×D4—41no—
563C22×D4—44no—
564C22×D4—44no—
565C22×D4C2×Dic6114yes—
566C22×D4C2×Dic6114yescomplemented
567C22×D4C22⋊D6111yescharacteristic
568C22×D4C22×D6111yescharacteristic
569C22×D4C22×D6111yescharacteristic
570C22×D4C22×D6111yescharacteristic
571C23×C4—21no—
572C23×C4—1221no—
573C23×C4C22×D6111yescharacteristic
574C23×C4C22×D6111yescharacteristic
575C2×M16—1222no—
576C2×M16—1222no—
577C2×M16—2441no—
578C22×C8—611no—
579C22×C8—611no—
580C22×C8—611no—
581C22×C8—611no—
582C22×C8—1222no—
583C22×C8—1222no—
584C22×C8—2441no—
585#127—22no—
586#127C2×Dic6114yescomplemented
587#121—22no—
588#121—22no—
589#121—28no—
590#121C2×Dic6114yes—
591#121C2×Dic6114yescomplemented
592#120—28no—
593#120—28no—
594C4×D4—22no—
595C4×D4C2×Dic6114yes—
596C4×D4C2×Dic6114yescomplemented
597C4×D4C22⋊D6114yes—
598#117—1222no—
599#117—2441no—
600C2×C4⋊C4—611no—
601C2×C4⋊C4—611no—
602C2×C4⋊C4—611no—
603C2×C4⋊C4—611no—
604C2×C4⋊C4—1222no—
605C2×C4⋊C4—1221no—
606C2×C4⋊C4—2441no—
607C2×C4⋊C4C22⋊D6111yescharacteristic
608C2×C4⋊C4C22×D6111yescharacteristic
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—1221no—
613C2×C22⋊C4—1221no—
614C2×C22⋊C4—1221no—
615C2×C22⋊C4C22⋊D6111yescharacteristic
616C2×C22⋊C4C22⋊D6111yescharacteristic
617C2×C42—1221no—
618C2×C42—1221no—
619C2×C42C22×D6111yescharacteristic
620C4⋊C8—1222no—
621#102—614no—
622#102—1222no—
623#102—1222no—
624#102—1222no—
625#102—1222no—
626#102—1222no—
627#102—1222no—
628#102—1222no—
629#102—2441no—
630#102—2441no—
631#102—2441no—
632#102—2441no—
633C22⋊C8—1222no—
634C22⋊C8—1222no—
635#97—1222no—
636#95—1221no—
637#95—1221no—
638#95—1221no—
639#95—1221no—
640#95—1221no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—24no—
645C24—24no—
646C24—42no—
647C24—42no—
648C24—42no—
649C24—42no—
650C24—42no—
651C24—42no—
652C24—42no—
653C24—42no—
654C24—81no—
655C24—81no—
656C24—81no—
657C24—81no—
658C24C2×C22⋊D6111yescharacteristic
659C24C2×C22⋊D6111yescharacteristic
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—28no—
663C2×D4—28no—
664C2×D4—24no—
665C2×D4—24no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—24no—
680C2×D4—24no—
681C2×D4—24no—
682C2×D4—24no—
683C2×D4—44no—
684C2×D4—44no—
685C2×D4—44no—
686C2×D4—44no—
687C2×D4—44no—
688C2×D4—44no—
689C2×D4—42no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—432no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—42no—
700C2×D4—81no—
701C2×D4—81no—
702C2×D4C22⋊Dic6114yes—
703C2×D4D4×D6112yes—
704C2×D4#1175822412yes—
705C2×D4C22×Dic6112yes—
706C2×D4C22×Dic6112yes—
707C2×D4C22×Dic6112yes—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—24no—
718C22×C4—42no—
719C22×C4—42no—
720C22×C4—1221no—
721C22×C4—1221no—
722C22×C4—1221no—
723C22×C4—1221no—
724C22×C4—4881no—
725C22×C4—2442no—
726C22×C4—2442no—
727C22×C4C22×Dic6112yes—
728C22×C4C22×Dic6112yes—
729C22×C4C2×C22⋊D6112yes—
730C22×C4C2×C22⋊D6112yes—
731C22×C4C2×C22⋊D6111yescharacteristic
732C22×C4C2×C22⋊D6111yescharacteristic
733C22×C4C2×C22⋊D6111yescharacteristic
734C22×C4C2×C22⋊D6111yescharacteristic
735C22×C4C23×D6111yescharacteristic
736M16—2444no—
737C2×C8—612no—
738C2×C8—1221no—
739C2×C8—1221no—
740C2×C8—1221no—
741C2×C8—1221no—
742C2×C8—1221no—
743C2×C8—1221no—
744C2×C8—1221no—
745C2×C8—1221no—
746C2×C8—1221no—
747C2×C8—1221no—
748C2×C8—1221no—
749C2×C8—2444no—
750C4⋊C4—21no—
751C4⋊C4—612no—
752C4⋊C4—1221no—
753C4⋊C4—1221no—
754C4⋊C4—1221no—
755C4⋊C4—1221no—
756C4⋊C4—1221no—
757C4⋊C4—1221no—
758C4⋊C4—1221no—
759C4⋊C4—2442no—
760C4⋊C4C22⋊Dic6114yes—
761C4⋊C4C22×Dic6112yes—
762C22⋊C4—24no—
763C22⋊C4—24no—
764C22⋊C4—24no—
765C22⋊C4—4881no—
766C22⋊C4—2442no—
767C22⋊C4—2442no—
768C22⋊C4C22⋊Dic6114yes—
769C22⋊C4C22⋊Dic6114yes—
770C42—4881no—
771C42—2442no—
772C42C22×Dic6112yes—
773C42C2×C22⋊D6112yes—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—22no—
779C23—21no—
780C23—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—22no—
785C23—21no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—48no—
790C23—48no—
791C23—48no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—48no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—84no—
810C23—84no—
811C23—84no—
812C23—84no—
813C23—84no—
814C23—84no—
815C23—84no—
816C23—84no—
817C23—84no—
818C23—84no—
819C23C2×C22⋊Dic6112yes—
820C23C2×C22⋊Dic6112yes—
821C23#1451980312yes—
822C23#1451980312yes—
823C23C22×C22⋊D6111yescharacteristic
824D4—28no—
825D4—22no—
826D4—22no—
827D4—22no—
828D4—22no—
829D4—22no—
830D4—22no—
831D4—22no—
832D4—48no—
833D4—48no—
834D4—48no—
835D4—48no—
836D4—48no—
837D4—41no—
838D4—41no—
839D4—41no—
840D4—41no—
841D4—84no—
842D4D4×Dic6114yes—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—48no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—1222no—
864C2×C4—4884no—
865C2×C4—2441no—
866C2×C4—2441no—
867C2×C4—2441no—
868C2×C4—2441no—
869C2×C4—2441no—
870C2×C4—2441no—
871C2×C4—2441no—
872C2×C4—2441no—
873C2×C4—2441no—
874C2×C4—2441no—
875C2×C4—2441no—
876C2×C4C2×C22⋊Dic6112yes—
877C2×C4C2×C22⋊Dic6112yes—
878C2×C4C2×C22⋊Dic6112yes—
879C2×C4C2×C22⋊Dic6112yes—
880C2×C4C23×Dic6111yescharacteristic
881C2×C4C2×D4×D6111yescharacteristic
882C2×C4C22×C22⋊D6111yescharacteristic
883C2×C4C2×#1175822411yescharacteristic
884C2×C4#1451982211yescharacteristic
885C2×C4#1451982211yescharacteristic
886C8—1222no—
887C8—2441no—
888C8—2441no—
889C8—2441no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—22no—
894C22—22no—
895C22—22no—
896C22—22no—
897C22—22no—
898C22—24no—
899C22—22no—
900C22—42no—
901C22—41no—
902C22—42no—
903C22—41no—
904C22—42no—
905C22—41no—
906C22—42no—
907C22—41no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—816no—
917C22—816no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22#1683976714yescomplemented
927C22C22×C22⋊Dic6111yescharacteristic
928C22D4×C22⋊D6111yescharacteristic
929C22#1684040611yescharacteristic
930C22C2×#1451980311yescharacteristic
931C22C2×#1451980311yescharacteristic
932C22#1684056511yescharacteristic
933C22#1684057311yescharacteristic
934C4—22no—
935C4—22no—
936C4—22no—
937C4—22no—
938C4—42no—
939C4—4881no—
940C4—4881no—
941C4—4881no—
942C4—2442no—
943C4C2×D4×Dic6111yescharacteristic
944C4#1684023711yescharacteristic
945C4D4×C22⋊D6111yescharacteristic
946C4#1684040611yescharacteristic
947C2—24no—
948C2—42no—
949C2—44no—
950C2—82no—
951C2—82no—
952C2D4×C22⋊Dic6111yescharacteristic
953C2C2×#1683976711yescharacteristic
954C2#2145434511yescharacteristic
955C2#2145729511yescharacteristic
956C2#2145731011yescharacteristic
957C2#2145784011yescharacteristic
958C2#2145796011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
Fitting, prime radicalC2×D42×C61C2
socleC23×C61C22×D4
cosocleC22×C4×C61C24
hypercenterC2×D42D61
hypocenterC61#22423
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×D42

Complements

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

NH ≅ G/Ntype
1. C2×#16839834C2semidirect
2. C2×#16839767C2semidirect
3. C22×#14519698C2semidirect
4. #21448748C2semidirect
5. #21446747C2semidirect
6. #21446644C2semidirect
7. #21446258C2semidirect
8. #21446248C2semidirect
9. #21446142C2semidirect
10. #21446137C2semidirect
11. #21445829C2semidirect
12. #21445750C2semidirect
13. #21445750C2semidirect
14. #21445644C2semidirect
16. C22×#11758194C22semidirect
17. C23×#92418C22semidirect
18. C2×#14519736C22semidirect
19. C22×C4⋊Dic61C22semidirect
21. C2×C4⋊#92418C22semidirect
28. C2×#14519698C22semidirect
29. C2×#14519698C22semidirect
30. C2×#14519698C22semidirect
31. C2×#14519698C22semidirect
32. C2×#14519698C22semidirect
33. C2×#14519698C22semidirect
34. C2×#14519698C22semidirect
35. C2×#14519698C22semidirect
36. C2×C22⋊#92418C22semidirect
37. C2×C22⋊#92418C22semidirect
38. C2×#14519688C22semidirect
42. #16839628C22semidirect
43. #16839622C22semidirect
44. #16839622C22semidirect
45. C4×C4⋊Dic61C22semidirect
47. #16839524C22semidirect
48. #16839524C22semidirect
49. #16839524C22semidirect
50. #16839524C22semidirect
55. D42×C61C4semidirect
101. #14519698D4semidirect
132. C22×D4×C61C2×C4semidirect
141. #127×C61C2×C4semidirect
146. #121×C61C2×C4semidirect
151. C4×D4×C61C2×C4semidirect
277. C4⋊Dic61C2×D4semidirect
293. C2×#92418C2×D4semidirect
447. C22×C61#418semidirect
501. D42Dic61semidirect
543. C61#22423semidirect
566. C22×D4C2×Dic61semidirect
586. #127C2×Dic61semidirect
591. #121C2×Dic61semidirect
596. C4×D4C2×Dic61semidirect
926. C22#16839767semidirect

Maximal subgroups

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

subgroupindex
C2×#168398342
C2×#168397672
C22×#145196982
#214487482
#214467472
#214466442
#214462582
#214462482
#214461422
#214461372
#214458292
#214457502
#214456442
C2×D42×C612
#2242361