Finite Group Databasebeta

← #29717574

Subgroups — #29717574

Order 15616.

1992 conjugacy classes of subgroups.

The subgroup lattice has 1036 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839996C211yesmaximal, characteristic, complemented
2C2×#16839896C211yesmaximal, characteristic, complemented
3C2×#16839896C211yesmaximal, characteristic, complemented
4C22×#14519698C211yesmaximal, characteristic, complemented
5#21449259C211yesmaximal, characteristic, complemented
6#21447050C211yesmaximal, characteristic, complemented
7#21446998C211yesmaximal, characteristic, complemented
8#21446890C211yesmaximal, characteristic, complemented
9#21446815C211yesmaximal, characteristic, complemented
10#21446167C211yesmaximal, characteristic, complemented
11#21446137C211yesmaximal, characteristic, complemented
12#21446112C211yesmaximal, characteristic, complemented
13#21446066C211yesmaximal, characteristic, complemented
14#21445750C211yesmaximal, characteristic, complemented
15C2×D42×C61C211yesmaximal, characteristic, complemented
16C22×#11758199C2211yescharacteristic
17C22×#11758199C2211yescharacteristic, complemented
18C22×#11758199C2211yescharacteristic, complemented
19C23×#92418C2211yescharacteristic, complemented
20C2×#14519751C2211yescharacteristic, complemented
21C2×#14519751C2211yescharacteristic, complemented
22C2×#14519749—21no—
23C22×C4⋊Dic61C2211yescharacteristic, complemented
24#16839996—24no—
25#16839896—24no—
26#16839896—24no—
27C2×#14519710C2211yescharacteristic, complemented
28C2×#14519698—24no—
29C2×#14519698C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519698C2211yescharacteristic
32C2×#14519698C2211yescharacteristic, complemented
33C2×#14519698C2211yescharacteristic, complemented
34C2×#14519698C2211yescharacteristic, complemented
35C2×#14519698C2211yescharacteristic, complemented
36C2×#14519698C2211yescharacteristic, complemented
37C2×#14519698C2211yescharacteristic, complemented
38C2×#14519697C2211yescharacteristic, complemented
39C2×C22⋊#92418C2211yescharacteristic, complemented
40C2×C22⋊#92418C2211yescharacteristic, complemented
41C2×C22⋊#92418C2211yescharacteristic, complemented
42#16839684—21no—
43#16839678—21no—
44#16839664C2211yescharacteristic, complemented
45#16839660C2211yescharacteristic, complemented
46#16839639—21no—
47#16839622C2211yescharacteristic, complemented
48#16839524C2211yescharacteristic, complemented
49#16839524C2211yescharacteristic, complemented
50#16839517C2211yescharacteristic, complemented
51#16839517C2211yescharacteristic, complemented
52C23×D4×C61—21no—
53C23×D4×C61C2211yescharacteristic
54C23×D4×C61C2211yescharacteristic
55D42×C61—24no—
56D42×C61—24no—
57C2×#127×C61C2211yescharacteristic
58C2×#121×C61—21no—
59C2×#121×C61C2211yescharacteristic
60C2×#121×C61C2211yescharacteristic
61C2×#120×C61—21no—
62C2×#120×C61—21no—
63C2×C4×D4×C61C2211yescharacteristic
64C2×C4×D4×C61C2211yescharacteristic
65C22×D244C2311yescharacteristic
66C22×C22⋊D61—21no—
67C22×C22⋊D61—21no—
68C23×Dic61—21no—
69C2×#11758199—22no—
70C2×#11758199—22no—
71C2×#11758199—22no—
72C2×#11758199—22no—
73C2×#11758199—22no—
74C2×#11758199—22no—
75C2×#11758199—41no—
76C2×#11758199—41no—
77C2×#11758199—41no—
78C22×#92418—22no—
79C22×#92418—22no—
80C22×#92418—41no—
81C22×#92418C2311yescharacteristic
82C22×#92418C2311yescharacteristic
83C22×#92418C2311yescharacteristic
84C22×#92418C2311yescharacteristic
85#14519751—22no—
86#14519751—22no—
87#14519751—22no—
88#14519751—41no—
89#14519749—44no—
90C2×C4⋊Dic61—22no—
91C2×C4⋊Dic61—21no—
92C2×C4⋊Dic61—41no—
93C2×C4⋊Dic61C2311yescharacteristic
94C2×C4⋊Dic61C2311yescharacteristic
95C2×C4⋊Dic61C2311yescharacteristic
96C2×#11758196—21no—
97C2×C22⋊Dic61—21no—
98C2×#11758198—21no—
99C2×#11758198—21no—
100C2×#11758198—21no—
101C2×#11758198—21no—
102#14519710—22no—
103#14519698—22no—
104#14519698—22no—
105#14519698—22no—
106#14519698—22no—
107#14519698—22no—
108#14519698—22no—
109#14519698—22no—
110#14519698—41no—
111#14519698D414yescomplemented
112#14519697—22no—
113C22⋊#92418—22no—
114C22⋊#92418—22no—
115C22⋊#92418—41no—
116#14519684—21no—
117#14519684—21no—
118C25×C61—21no—
119C25×C61—21no—
120C22×D4×C61—22no—
121C22×D4×C61—22no—
122C22×D4×C61—28no—
123C22×D4×C61—21no—
124C22×D4×C61—21no—
125C22×D4×C61—22no—
126C22×D4×C61—22no—
127C22×D4×C61—22no—
128C22×D4×C61—22no—
129C22×D4×C61—21no—
130C22×D4×C61—22no—
131C22×D4×C61—21no—
132C22×D4×C61—21no—
133C22×D4×C61—21no—
134C22×D4×C61—41no—
135C22×D4×C61—41no—
136C22×D4×C61—41no—
137C22×D4×C61—41no—
138C22×D4×C61—44no—
139C22×D4×C61—44no—
140C22×D4×C61D411yescharacteristic
141C22×D4×C61D414yescomplemented
142C22×D4×C61C2311yescharacteristic
143C22×D4×C61C2311yescharacteristic
144C22×D4×C61C2311yescharacteristic
145C23×C4×C61—21no—
146C23×C4×C61C2311yescharacteristic
147C23×C4×C61C2311yescharacteristic
148#127×C61—22no—
149#127×C61—22no—
150#121×C61—28no—
151#121×C61—22no—
152#121×C61—22no—
153#121×C61—22no—
154#121×C61D414yescomplemented
155#120×C61—28no—
156#120×C61—28no—
157C4×D4×C61—22no—
158C4×D4×C61—22no—
159C4×D4×C61—22no—
160C4×D4×C61—22no—
161C2×C4⋊C4×C61D411yescharacteristic
162C2×C4⋊C4×C61C2311yescharacteristic
163C2×C22⋊C4×C61—21no—
164C2×C22⋊C4×C61—21no—
165C2×C22⋊C4×C61—21no—
166C2×C22⋊C4×C61D411yescharacteristic
167C2×C22⋊C4×C61D411yescharacteristic
168C2×C42×C61C2311yescharacteristic
169C24×C61—21no—
170C24×C61—24no—
171C24×C61—21no—
172C24×C61—21no—
173C24×C61—24no—
174C24×C61—42no—
175C24×C61—42no—
176C24×C61—42no—
177C24×C61—42no—
178C24×C61—42no—
179C24×C61—42no—
180C24×C61—42no—
181C24×C61—42no—
182C24×C61—81no—
183C24×C61—81no—
184C24×C61—81no—
185C24×C61—81no—
186C24×C61C2×D411yescharacteristic
187C24×C61C2×D411yescharacteristic
188C23×D61—21no—
189C2×D4×C61—22no—
190C2×D4×C61—22no—
191C2×D4×C61—28no—
192C2×D4×C61—24no—
193C2×D4×C61—24no—
194C2×D4×C61—24no—
195C2×D4×C61—24no—
196C2×D4×C61—24no—
197C2×D4×C61—24no—
198C2×D4×C61—21no—
199C2×D4×C61—21no—
200C2×D4×C61—21no—
201C2×D4×C61—21no—
202C2×D4×C61—21no—
203C2×D4×C61—21no—
204C2×D4×C61—21no—
205C2×D4×C61—21no—
206C2×D4×C61—21no—
207C2×D4×C61—21no—
208C2×D4×C61—21no—
209C2×D4×C61—21no—
210C2×D4×C61—21no—
211C2×D4×C61—44no—
212C2×D4×C61—44no—
213C2×D4×C61—44no—
214C2×D4×C61—42no—
215C2×D4×C61—42no—
216C2×D4×C61—42no—
217C2×D4×C61—42no—
218C2×D4×C61—42no—
219C2×D4×C61—44no—
220C2×D4×C61—44no—
221C2×D4×C61—432no—
222C2×D4×C61—44no—
223C2×D4×C61—42no—
224C2×D4×C61—42no—
225C2×D4×C61—42no—
226C2×D4×C61—42no—
227C2×D4×C61—44no—
228C2×D4×C61—42no—
229C2×D4×C61—81no—
230C2×D4×C61—81no—
231C2×D4×C61D814yescomplemented
232C2×D4×C61C2×D412yes—
233C2×D4×C61C2×D412yes—
234C2×D4×C61C2×D412yes—
235C2×D4×C61C2×D412yes—
236C2×D4×C61#4112yes—
237C22×C4×C61—21no—
238C22×C4×C61—21no—
239C22×C4×C61—21no—
240C22×C4×C61—21no—
241C22×C4×C61—24no—
242C22×C4×C61—21no—
243C22×C4×C61—21no—
244C22×C4×C61—21no—
245C22×C4×C61—21no—
246C22×C4×C61—21no—
247C22×C4×C61—21no—
248C22×C4×C61—21no—
249C22×C4×C61—42no—
250C22×C4×C61—42no—
251C22×C4×C61C2×D411yescharacteristic
252C22×C4×C61C2×D411yescharacteristic
253C22×C4×C61C2×D411yescharacteristic
254C22×C4×C61C2×D412yes—
255C22×C4×C61C2×D412yes—
256C22×C4×C61C2×D411yescharacteristic
257C22×C4×C61C2411yescharacteristic
258C2×C22⋊D61—42no—
259C2×C22⋊D61—42no—
260C2×C22⋊D61—42no—
261C2×C22⋊D61—42no—
262C2×C22⋊D61—42no—
263C2×C22⋊D61—81no—
264C22×Dic61—21no—
265C22×Dic61—21no—
266C22×Dic61—21no—
267C22×Dic61—42no—
268C22×Dic61—42no—
269C22×Dic61—81no—
270C2×D244—21no—
271C2×D244—21no—
272C2×D244—21no—
273C2×D244—21no—
274C2×D244—21no—
275C2×D244—21no—
276C4⋊C4×C61—22no—
277C4⋊C4×C61—21no—
278C4⋊C4×C61C2×D412yes—
279C22⋊C4×C61—24no—
280C22⋊C4×C61—24no—
281C22⋊C4×C61—22no—
282C22⋊C4×C61—24no—
283C22⋊C4×C61—22no—
284C42×C61—21no—
285C42×C61—21no—
286C22⋊Dic61—42no—
287#11758199—44no—
288#11758199—44no—
289#11758199—44no—
290#11758198—42no—
291#11758198—42no—
292#11758198—42no—
293#11758198—81no—
294C4⋊Dic61—21no—
295C4⋊Dic61—21no—
296C4⋊Dic61—21no—
297C4⋊Dic61—21no—
298C4⋊Dic61—21no—
299C4⋊Dic61—42no—
300C4⋊Dic61C2×D412yescomplemented
301#11758196—42no—
302C2×#92418—21no—
303C2×#92418—21no—
304C2×#92418—21no—
305C2×#92418—21no—
306C2×#92418—21no—
307C2×#92418—21no—
308C2×#92418—21no—
309C2×#92418—21no—
310C2×#92418—21no—
311C2×#92418—21no—
312C2×#92418—21no—
313C2×#92418—44no—
314C2×#92418C2×D412yescomplemented
315C23×C61—21no—
316C23×C61—21no—
317C23×C61—21no—
318C23×C61—21no—
319C23×C61—21no—
320C23×C61—22no—
321C23×C61—21no—
322C23×C61—22no—
323C23×C61—21no—
324C23×C61—22no—
325C23×C61—21no—
326C23×C61—21no—
327C23×C61—21no—
328C23×C61—22no—
329C23×C61—22no—
330C23×C61—48no—
331C23×C61—48no—
332C23×C61—48no—
333C23×C61—41no—
334C23×C61—41no—
335C23×C61—41no—
336C23×C61—41no—
337C23×C61—41no—
338C23×C61—41no—
339C23×C61—41no—
340C23×C61—41no—
341C23×C61—41no—
342C23×C61—41no—
343C23×C61—41no—
344C23×C61—41no—
345C23×C61—41no—
346C23×C61—41no—
347C23×C61—41no—
348C23×C61—41no—
349C23×C61—48no—
350C23×C61—84no—
351C23×C61—84no—
352C23×C61—84no—
353C23×C61—84no—
354C23×C61—84no—
355C23×C61—84no—
356C23×C61—84no—
357C23×C61—84no—
358C23×C61—84no—
359C23×C61—84no—
360C23×C61#12012yes—
361C23×C61C2×D812yes—
362C23×C61C2×D812yes—
363C23×C61AGL(1,ℤ/8)12yes—
364C23×C61C22×D411yescharacteristic
365C22×D61—41no—
366C22×D61—41no—
367C22×D61—41no—
368C22×D61—41no—
369C22×D61—41no—
370C22×D61—41no—
371C22×D61—41no—
372D4×C61—28no—
373D4×C61—22no—
374D4×C61—22no—
375D4×C61—22no—
376D4×C61—22no—
377D4×C61—22no—
378D4×C61—22no—
379D4×C61—22no—
380D4×C61—48no—
381D4×C61—48no—
382D4×C61—48no—
383D4×C61—48no—
384D4×C61—48no—
385D4×C61—41no—
386D4×C61—41no—
387D4×C61—41no—
388D4×C61—41no—
389D4×C61—84no—
390D4×C61#12114yescomplemented
391C2×C4×C61—21no—
392C2×C4×C61—21no—
393C2×C4×C61—21no—
394C2×C4×C61—21no—
395C2×C4×C61—22no—
396C2×C4×C61—22no—
397C2×C4×C61—22no—
398C2×C4×C61—22no—
399C2×C4×C61—21no—
400C2×C4×C61—21no—
401C2×C4×C61—22no—
402C2×C4×C61—21no—
403C2×C4×C61—21no—
404C2×C4×C61—21no—
405C2×C4×C61—21no—
406C2×C4×C61—48no—
407C2×C4×C61—41no—
408C2×C4×C61—41no—
409C2×C4×C61—41no—
410C2×C4×C61—41no—
411C2×C4×C61—41no—
412C2×C4×C61—41no—
413C2×C4×C61#12012yes—
414C2×C4×C61C2×D812yes—
415C2×C4×C61C22×D411yescharacteristic
416C2×C4×C61C22×D411yescharacteristic
417C2×C4×C61C22×D411yescharacteristic
418C2×C4×C61C2×#4111yescharacteristic
419C2×C4×C61H(5,𝔽2)11yescharacteristic
420C2×C4×C61H(5,𝔽2)11yescharacteristic
421C22⋊D61—84no—
422C22⋊D61—84no—
423C2×Dic61—22no—
424C2×Dic61—41no—
425C2×Dic61—41no—
426C2×Dic61—41no—
427C2×Dic61—41no—
428C2×Dic61—41no—
429C2×Dic61—41no—
430C2×Dic61—41no—
431C2×Dic61—41no—
432C2×Dic61—84no—
433D244—41no—
434D244—41no—
435D244—41no—
436D244—41no—
437#92418—22no—
438#92418—41no—
439#92418—41no—
440#92418—41no—
441#24424—611nomaximal, Sylow
442C22×C61—22no—
443C22×C61—22no—
444C22×C61—22no—
445C22×C61—22no—
446C22×C61—22no—
447C22×C61—22no—
448C22×C61—24no—
449C22×C61—22no—
450C22×C61—22no—
451C22×C61—22no—
452C22×C61—41no—
453C22×C61—42no—
454C22×C61—41no—
455C22×C61—42no—
456C22×C61—41no—
457C22×C61—42no—
458C22×C61—42no—
459C22×C61—42no—
460C22×C61—41no—
461C22×C61—42no—
462C22×C61—42no—
463C22×C61—42no—
464C22×C61—42no—
465C22×C61—42no—
466C22×C61—42no—
467C22×C61—42no—
468C22×C61—816no—
469C22×C61—816no—
470C22×C61—81no—
471C22×C61—81no—
472C22×C61—81no—
473C22×C61—81no—
474C22×C61—81no—
475C22×C61—81no—
476C22×C61—81no—
477C22×C61—81no—
478C22×C61#44714yescomplemented
479C22×C61C2×#12011yescharacteristic
480C22×C61D4211yescharacteristic
481C22×C61#54611yescharacteristic
482C22×C61C22×D811yescharacteristic
483C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
484C22×C61#57611yescharacteristic
485C22×C61#57711yescharacteristic
486C2×D61—81no—
487C2×D61—81no—
488C2×D61—81no—
489C2×D61—81no—
490C2×D61—81no—
491C2×D61—81no—
492C2×D61—81no—
493C4×C61—22no—
494C4×C61—22no—
495C4×C61—41no—
496C4×C61—42no—
497C4×C61—41no—
498C4×C61C2×#12111yescharacteristic
499C4×C61#53411yescharacteristic
500C4×C61D4211yescharacteristic
501C4×C61#54611yescharacteristic
502Dic61—42no—
503Dic61—81no—
504Dic61—81no—
505C2×D42D6111yescharacteristic, complemented
506C2×#466—611no—
507C2×#447—611no—
508C2×#447—611no—
509C22×#102—611no—
510#2416—611no—
511#2041—611no—
512#2033—611no—
513#2011—611no—
514#1999—611no—
515#1879—611no—
516#1874—611no—
517#1869—611no—
518#1862—611no—
519#1786—611no—
520C2×C61—24no—
521C2×C61—42no—
522C2×C61—44no—
523C2×C61—82no—
524C2×C61—82no—
525C2×C61#241011yescharacteristic
526C2×C61C2×#44711yescharacteristic
527C2×C61#301211yescharacteristic
528C2×C61#326511yescharacteristic
529C2×C61D4×D811yescharacteristic
530C2×C61#329411yescharacteristic
531C2×C61#331811yescharacteristic
532D61—161no—
533C23×D4—21no—
534C23×D4C2×D6111yescharacteristic
535C23×D4C2×D6111yescharacteristic
536C22×D8—611no—
537C22×D8—611no—
538C22×D8—611no—
539C23×C8—611no—
540D42—24no—
541D42—24no—
542C2×#127C2×D6111yescharacteristic
543C2×#121—21no—
544C2×#121—611no—
545C2×#121—611no—
546C2×#121—1221no—
547C2×#121C2×D6111yescharacteristic
548C2×#121C2×D6111yescharacteristic
549C2×#120—21no—
550C2×#120—21no—
551C2×C4×D4C2×D6111yescharacteristic
552C2×C4×D4C2×D6111yescharacteristic
553C22×C4⋊C4—611no—
554#466—1224no—
555#447—1224no—
556#447—1224no—
557C2×#107—611no—
558C2×#102—611no—
559C2×#102—611no—
560C2×#102—611no—
561C2×#102—611no—
562C2×#102—611no—
563C2×#102—611no—
564C2×#102—611no—
565C2×#102—611no—
566C2×#102—611no—
567C2×#102—611no—
568C2×#102—1224no—
569C2×C22⋊C8—611no—
570C2×C22⋊C8—611no—
571C2×C22⋊C8—611no—
572#396—1221no—
573#394—1221no—
574#390—611no—
575#389—611no—
576#386—1221no—
577#380—611no—
578#340—611no—
579#340—611no—
580#336—611no—
581#336—611no—
582C61#2442411yescharacteristic, complemented, Sylow
583C25—21no—
584C25—21no—
585C22×D4—22no—
586C22×D4—22no—
587C22×D4—28no—
588C22×D4—21no—
589C22×D4—21no—
590C22×D4—22no—
591C22×D4—22no—
592C22×D4—22no—
593C22×D4—22no—
594C22×D4—21no—
595C22×D4—21no—
596C22×D4—21no—
597C22×D4—22no—
598C22×D4—21no—
599C22×D4—41no—
600C22×D4—41no—
601C22×D4—41no—
602C22×D4—41no—
603C22×D4—44no—
604C22×D4—44no—
605C22×D4—611no—
606C22×D4—1221no—
607C22×D4—1221no—
608C22×D4C22⋊D6111yescharacteristic
609C22×D4C22⋊D6114yescomplemented
610C22×D4C22×D6111yescharacteristic
611C22×D4C22×D6111yescharacteristic
612C22×D4C22×D6111yescharacteristic
613C23×C4—21no—
614C23×C4—1221no—
615C23×C4C22×D6111yescharacteristic
616C23×C4C22×D6111yescharacteristic
617C2×D8—1222no—
618C2×D8—1222no—
619C2×D8—1222no—
620C2×D8—1222no—
621C2×D8—1222no—
622C2×D8—1222no—
623C2×D8—2441no—
624C2×D8—2441no—
625C2×D8—2441no—
626C22×C8—611no—
627C22×C8—611no—
628C22×C8—611no—
629C22×C8—611no—
630C22×C8—1222no—
631C22×C8—1222no—
632C22×C8—2441no—
633#127—22no—
634#127—22no—
635#121—28no—
636#121—22no—
637#121—22no—
638#121—22no—
639#121—1222no—
640#121—1222no—
641#121—1222no—
642#121—2441no—
643#121—2444no—
644#121C22⋊D6114yescomplemented
645#120—28no—
646#120—28no—
647C4×D4—22no—
648C4×D4—22no—
649C4×D4—22no—
650C4×D4—22no—
651C2×C4⋊C4—611no—
652C2×C4⋊C4—611no—
653C2×C4⋊C4—611no—
654C2×C4⋊C4—1222no—
655C2×C4⋊C4—1221no—
656C2×C4⋊C4—1221no—
657C2×C4⋊C4—2441no—
658C2×C4⋊C4C22⋊D6111yescharacteristic
659C2×C4⋊C4C22×D6111yescharacteristic
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—1221no—
664C2×C22⋊C4—1221no—
665C2×C22⋊C4—1221no—
666C2×C22⋊C4—1221no—
667C2×C22⋊C4—1221no—
668C2×C22⋊C4C22⋊D6111yescharacteristic
669C2×C22⋊C4C22⋊D6111yescharacteristic
670C2×C42C22×D6111yescharacteristic
671#107—1222no—
672#102—614no—
673#102—1222no—
674#102—1222no—
675#102—1222no—
676#102—1222no—
677#102—1222no—
678#102—1222no—
679#102—1222no—
680#102—1222no—
681#102—2441no—
682C22⋊C8—1222no—
683C22⋊C8—1222no—
684C22⋊C8—2441no—
685#95—1221no—
686#95—1221no—
687C24—21no—
688C24—24no—
689C24—21no—
690C24—21no—
691C24—24no—
692C24—42no—
693C24—42no—
694C24—42no—
695C24—42no—
696C24—42no—
697C24—42no—
698C24—42no—
699C24—42no—
700C24—81no—
701C24—81no—
702C24—81no—
703C24—81no—
704C24—1221no—
705C24C2×C22⋊D6111yescharacteristic
706C24C2×C22⋊D6111yescharacteristic
707C2×D4—22no—
708C2×D4—22no—
709C2×D4—28no—
710C2×D4—24no—
711C2×D4—24no—
712C2×D4—24no—
713C2×D4—24no—
714C2×D4—24no—
715C2×D4—21no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—21no—
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—24no—
729C2×D4—44no—
730C2×D4—44no—
731C2×D4—44no—
732C2×D4—42no—
733C2×D4—42no—
734C2×D4—42no—
735C2×D4—42no—
736C2×D4—42no—
737C2×D4—44no—
738C2×D4—44no—
739C2×D4—432no—
740C2×D4—44no—
741C2×D4—42no—
742C2×D4—42no—
743C2×D4—42no—
744C2×D4—42no—
745C2×D4—44no—
746C2×D4—42no—
747C2×D4—81no—
748C2×D4—81no—
749C2×D4—1221no—
750C2×D4—1221no—
751C2×D4—1221no—
752C2×D4—1221no—
753C2×D4—1221no—
754C2×D4—1221no—
755C2×D4—4881no—
756C2×D4—2442no—
757C2×D4—2442no—
758C2×D4—2442no—
759C2×D4—2442no—
760C2×D4—2442no—
761C2×D4#1175819914yescomplemented
762C2×D4D4×D6112yes—
763C2×D4#1175822412yes—
764C2×D4C2×C22⋊D6112yes—
765C2×D4C2×C22⋊D6112yes—
766C2×D4C2×C22⋊D6112yes—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—24no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—42no—
780C22×C4—42no—
781C22×C4—1221no—
782C22×C4—1221no—
783C22×C4—1221no—
784C22×C4—4881no—
785C22×C4—2442no—
786C22×C4—2442no—
787C22×C4C2×C22⋊D6111yescharacteristic
788C22×C4C2×C22⋊D6111yescharacteristic
789C22×C4C2×C22⋊D6112yes—
790C22×C4C2×C22⋊D6112yes—
791C22×C4C2×C22⋊D6111yescharacteristic
792C22×C4C2×C22⋊D6111yescharacteristic
793C22×C4C23×D6111yescharacteristic
794D8—2444no—
795D8—2444no—
796D8—2444no—
797C2×C8—612no—
798C2×C8—1221no—
799C2×C8—1221no—
800C2×C8—1221no—
801C2×C8—1221no—
802C2×C8—1221no—
803C2×C8—1221no—
804C2×C8—1221no—
805C2×C8—1221no—
806C2×C8—1221no—
807C2×C8—1221no—
808C2×C8—1221no—
809C2×C8—2444no—
810C4⋊C4—21no—
811C4⋊C4—22no—
812C4⋊C4—612no—
813C4⋊C4—1221no—
814C4⋊C4—1221no—
815C4⋊C4—1221no—
816C4⋊C4—1221no—
817C4⋊C4—1221no—
818C4⋊C4—2442no—
819C4⋊C4—2442no—
820C4⋊C4C2×C22⋊D6112yes—
821C22⋊C4—24no—
822C22⋊C4—24no—
823C22⋊C4—22no—
824C22⋊C4—24no—
825C22⋊C4—22no—
826C22⋊C4—4881no—
827C22⋊C4—2442no—
828C22⋊C4—2442no—
829C22⋊C4—2442no—
830C22⋊C4—2442no—
831C42—21no—
832C42—21no—
833C23—21no—
834C23—21no—
835C23—21no—
836C23—21no—
837C23—21no—
838C23—22no—
839C23—21no—
840C23—21no—
841C23—21no—
842C23—21no—
843C23—22no—
844C23—21no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—48no—
849C23—48no—
850C23—48no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—48no—
868C23—84no—
869C23—84no—
870C23—84no—
871C23—84no—
872C23—84no—
873C23—84no—
874C23—84no—
875C23—84no—
876C23—84no—
877C23—84no—
878C23—2441no—
879C23—2441no—
880C23—2441no—
881C23—2441no—
882C23—2441no—
883C23—2441no—
884C23—2441no—
885C23#1451974612yes—
886C23C2×#1175819912yes—
887C23C2×#1175819912yes—
888C23#1451980312yes—
889C23C22×C22⋊D6111yescharacteristic
890D4—28no—
891D4—22no—
892D4—22no—
893D4—22no—
894D4—22no—
895D4—22no—
896D4—22no—
897D4—22no—
898D4—48no—
899D4—48no—
900D4—48no—
901D4—48no—
902D4—48no—
903D4—41no—
904D4—41no—
905D4—41no—
906D4—41no—
907D4—84no—
908D4—4884no—
909D4—4884no—
910D4—2441no—
911D4—2441no—
912D4—2441no—
913D4—2441no—
914D4#1451974914yescomplemented
915C2×C4—21no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—22no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—48no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—1222no—
938C2×C4—4884no—
939C2×C4—2441no—
940C2×C4—2441no—
941C2×C4—2441no—
942C2×C4—2441no—
943C2×C4—2441no—
944C2×C4—2441no—
945C2×C4—2441no—
946C2×C4—2441no—
947C2×C4#1451974612yes—
948C2×C4C2×#1175819912yes—
949C2×C4C2×D4×D6111yescharacteristic
950C2×C4C22×C22⋊D6111yescharacteristic
951C2×C4C22×C22⋊D6111yescharacteristic
952C2×C4C2×#1175822411yescharacteristic
953C2×C4#1451982211yescharacteristic
954C2×C4#1451982211yescharacteristic
955C8—1222no—
956C8—2441no—
957C8—2441no—
958C8—2441no—
959C22—22no—
960C22—22no—
961C22—22no—
962C22—22no—
963C22—22no—
964C22—22no—
965C22—22no—
966C22—22no—
967C22—22no—
968C22—24no—
969C22—41no—
970C22—42no—
971C22—41no—
972C22—42no—
973C22—42no—
974C22—42no—
975C22—41no—
976C22—42no—
977C22—42no—
978C22—41no—
979C22—42no—
980C22—42no—
981C22—42no—
982C22—42no—
983C22—42no—
984C22—42no—
985C22—816no—
986C22—816no—
987C22—81no—
988C22—81no—
989C22—81no—
990C22—81no—
991C22—81no—
992C22—81no—
993C22—81no—
994C22—81no—
995C22—4881no—
996C22—4881no—
997C22—4881no—
998C22—4881no—
999C22—4881no—
1000C22—4881no—
1001C22—4881no—
1002C22#1683989614yescomplemented
1003C22C2×#1451974611yescharacteristic
1004C22D4×C22⋊D6111yescharacteristic
1005C22#1684040611yescharacteristic
1006C22C22×#1175819911yescharacteristic
1007C22C2×#1451980311yescharacteristic
1008C22#1684056511yescharacteristic
1009C22#1684057311yescharacteristic
1010C4—22no—
1011C4—22no—
1012C4—41no—
1013C4—42no—
1014C4—41no—
1015C4—4881no—
1016C4—4881no—
1017C4—2442no—
1018C4C2×#1451974911yescharacteristic
1019C4#1684032111yescharacteristic
1020C4D4×C22⋊D6111yescharacteristic
1021C4#1684040611yescharacteristic
1022C2—24no—
1023C2—42no—
1024C2—44no—
1025C2—82no—
1026C2—82no—
1027C2—9761no—
1028C2#2144919311yescharacteristic
1029C2C2×#1683989611yescharacteristic
1030C2#2145512311yescharacteristic
1031C2#2145731011yescharacteristic
1032C2D4×#1175819911yescharacteristic
1033C2#2145763211yescharacteristic
1034C2#2145796011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×D42×C61C2
socleC23×C61C22×D4
hypercenterC2×D42D61
hypocenterC61#24424
LCSG ▷ C22×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×#16839996C2semidirect
2. C2×#16839896C2semidirect
3. C2×#16839896C2semidirect
4. C22×#14519698C2semidirect
5. #21449259C2semidirect
6. #21447050C2semidirect
7. #21446998C2semidirect
8. #21446890C2semidirect
9. #21446815C2semidirect
10. #21446167C2semidirect
11. #21446137C2semidirect
12. #21446112C2semidirect
13. #21446066C2semidirect
14. #21445750C2semidirect
15. C2×D42×C61C2semidirect
17. C22×#11758199C22semidirect
18. C22×#11758199C22semidirect
19. C23×#92418C22semidirect
20. C2×#14519751C22semidirect
21. C2×#14519751C22semidirect
23. C22×C4⋊Dic61C22semidirect
27. C2×#14519710C22semidirect
32. C2×#14519698C22semidirect
33. C2×#14519698C22semidirect
34. C2×#14519698C22semidirect
35. C2×#14519698C22semidirect
36. C2×#14519698C22semidirect
37. C2×#14519698C22semidirect
38. C2×#14519697C22semidirect
39. C2×C22⋊#92418C22semidirect
40. C2×C22⋊#92418C22semidirect
41. C2×C22⋊#92418C22semidirect
44. #16839664C22semidirect
45. #16839660C22semidirect
47. #16839622C22semidirect
48. #16839524C22semidirect
49. #16839524C22semidirect
50. #16839517C22semidirect
51. #16839517C22semidirect
111. #14519698D4semidirect
141. C22×D4×C61D4semidirect
154. #121×C61D4semidirect
231. C2×D4×C61D8semidirect
300. C4⋊Dic61C2×D4semidirect
314. C2×#92418C2×D4semidirect
390. D4×C61#121semidirect
478. C22×C61#447semidirect
505. C2×D42D61semidirect
582. C61#24424semidirect
609. C22×D4C22⋊D61semidirect
644. #121C22⋊D61semidirect
761. C2×D4#11758199semidirect
914. D4#14519749semidirect
1002. C22#16839896semidirect

Maximal subgroups

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

subgroupindex
C2×#168399962
C2×#168398962
C22×#145196982
#214492592
#214470502
#214469982
#214468902
#214468152
#214461672
#214461372
#214461122
#214460662
#214457502
C2×D42×C612
#2442461