Finite Group Databasebeta

← #29707502

Subgroups — #29707502

Order 15616.

1902 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#121×D61C211yesmaximal, characteristic
2C2×#16839801C211yesmaximal, characteristic, complemented
3C2×#16839765C211yesmaximal, characteristic, complemented
4C2×#16839765C211yesmaximal, characteristic, complemented
5C2×#16839724C211yesmaximal, characteristic, complemented
6#21448201C211yesmaximal, characteristic, complemented
7#21447010C211yesmaximal, characteristic, complemented
8#21447008C211yesmaximal, characteristic, complemented
9#21447006C211yesmaximal, characteristic, complemented
10#21447004C211yesmaximal, characteristic, complemented
11#21447002C211yesmaximal, characteristic, complemented
12#21447000C211yesmaximal, characteristic, complemented
13#21446998C211yesmaximal, characteristic, complemented
14#21445537C211yesmaximal, characteristic, complemented
15C61×#2034C211yesmaximal, characteristic, complemented
16C22×D4×D61—21no—
17C22×D4×D61C2211yescharacteristic
18C23×C4×D61C2211yescharacteristic
19C22×#11758189C2211yescharacteristic
20C22×#11758189C2211yescharacteristic
21C2×#14519752C2211yescharacteristic
22C2×#14519751C2211yescharacteristic
23C2×#14519750—21no—
24C2×#14519749—21no—
25C2×#14519748C2211yescharacteristic
26#121×D61—24no—
27#121×D61—24no—
28C2×#14519735C2211yescharacteristic
29C2×#14519735C2211yescharacteristic
30C2×C4⋊C4×D61C2211yescharacteristic
31C2×C22⋊C4×D61—21no—
32#16839801—24no—
33C2×#14519711C2211yescharacteristic, complemented
34C2×#14519710C2211yescharacteristic, complemented
35C2×#14519708C2211yescharacteristic, complemented
36#16839765—24no—
37#16839765—24no—
38C2×#14519699C2211yescharacteristic, complemented
39C2×#14519699C2211yescharacteristic, complemented
40C2×#14519698C2211yescharacteristic, complemented
41C2×#14519698C2211yescharacteristic, complemented
42C2×#14519697C2211yescharacteristic, complemented
43C2×#14519697C2211yescharacteristic, complemented
44#16839724—24no—
45C2×C22⋊#92418C2211yescharacteristic, complemented
46C2×#14519689C2211yescharacteristic, complemented
47C2×#14519689C2211yescharacteristic, complemented
48#16839624—21no—
49#16839622C2211yescharacteristic, complemented
50#16839619C2211yescharacteristic, complemented
51#16839619C2211yescharacteristic, complemented
52#16839617—21no—
53C22⋊C4×Dic61—21no—
54#16839609—21no—
55#16839525C2211yescharacteristic, complemented
56#16839524C2211yescharacteristic, complemented
57#16839524C2211yescharacteristic, complemented
58C2×#121×C61C2211yescharacteristic
59C2×#106×C61C2211yescharacteristic, complemented
60C2×#102×C61C2211yescharacteristic, complemented
61C2×#102×C61C2211yescharacteristic, complemented
62C2×C22⋊C8×C61C2211yescharacteristic, complemented
63C61×#380C2211yescharacteristic, complemented
64C61×#340C2211yescharacteristic, complemented
65C24×D61—21no—
66C24×D61D411yescharacteristic
67C22×D244—21no—
68C22×D244C2311yescharacteristic
69C22×C22⋊D61—21no—
70C22×C22⋊D61—21no—
71C22×C22⋊D61—21no—
72C2×D4×D61—28no—
73C2×D4×D61—22no—
74C2×D4×D61—22no—
75C2×D4×D61—22no—
76C2×D4×D61—22no—
77C2×D4×D61—22no—
78C2×D4×D61—44no—
79C2×D4×D61—44no—
80C2×D4×D61D414yes—
81C23×Dic61D411yescharacteristic
82C22×C4×D61—21no—
83C22×C4×D61—22no—
84C22×C4×D61—22no—
85C22×C4×D61—22no—
86C22×C4×D61—22no—
87C22×C4×D61—22no—
88C22×C4×D61—22no—
89C22×C4×D61D411yescharacteristic
90C22×C4×D61D411yescharacteristic
91C22×C4×D61C2311yescharacteristic
92C22×C4×D61C2311yescharacteristic
93C2×#11758189—22no—
94C2×#11758189—22no—
95C2×#11758189—22no—
96C2×#11758189—22no—
97C2×#11758189—22no—
98C2×#11758189D414yescomplemented
99C22×#92418C2311yescharacteristic
100C22×#92418C2311yescharacteristic
101#14519752—22no—
102#14519752—22no—
103#14519751—22no—
104#14519751—22no—
105#14519750—28no—
106#14519749—28no—
107#14519748—22no—
108#14519748—22no—
109#14519735—22no—
110#14519735—22no—
111#14519735—22no—
112#14519735—22no—
113C2×C4⋊Dic61C2311yescharacteristic
114C2×C4⋊Dic61C2311yescharacteristic
115C2×C4⋊Dic61C2311yescharacteristic
116C2×#11758196—21no—
117C4⋊C4×D61—22no—
118C4⋊C4×D61D414yes—
119C2×C22⋊Dic61—21no—
120C2×C22⋊Dic61—21no—
121C2×#11758198—21no—
122C2×#11758198—21no—
123C2×#11758198—21no—
124C2×#11758198—21no—
125C2×#11758198—21no—
126C2×#11758198—21no—
127C22⋊C4×D61—28no—
128C2×C4×Dic61—21no—
129C2×C4×Dic61—21no—
130#14519711—22no—
131#14519710—22no—
132#14519708—22no—
133#14519699—22no—
134#14519699—22no—
135#14519698—22no—
136#14519698—22no—
137#14519697—22no—
138#14519697—22no—
139C22⋊#92418—22no—
140#14519689—22no—
141#14519689—22no—
142#14519684—21no—
143#14519684—21no—
144#14519684—21no—
145C22×D4×C61—21no—
146C22×D4×C61C2311yescharacteristic
147C23×C4×C61C2311yescharacteristic
148C22×C8×C61C2311yescharacteristic
149C22×C8×C61C2311yescharacteristic
150#121×C61—22no—
151#121×C61—22no—
152C2×C4⋊C4×C61C2311yescharacteristic
153C2×C4⋊C4×C61C2311yescharacteristic
154C2×C4⋊C4×C61C2311yescharacteristic
155C2×C22⋊C4×C61—21no—
156C2×C22⋊C4×C61—21no—
157#106×C61—22no—
158#102×C61—22no—
159#102×C61—22no—
160C22⋊C8×C61—22no—
161#95×C61—21no—
162C24×C61—21no—
163C24×C61C2×D411yescharacteristic
164C23×D61—22no—
165C23×D61—22no—
166C23×D61—22no—
167C23×D61—21no—
168C23×D61—24no—
169C23×D61—22no—
170C23×D61—22no—
171C23×D61—41no—
172C23×D61—41no—
173C23×D61—42no—
174C23×D61—42no—
175C23×D61—42no—
176C23×D61—42no—
177C23×D61—42no—
178C23×D61—42no—
179C23×D61C2×D411yescharacteristic
180C23×D61C2×D411yescharacteristic
181C2×D4×C61—24no—
182C2×D4×C61—21no—
183C2×D4×C61—21no—
184C2×D4×C61—21no—
185C2×D4×C61—21no—
186C2×D4×C61—21no—
187C2×D4×C61—42no—
188C2×D4×C61—42no—
189C2×D4×C61C2×D412yes—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61C2×D411yescharacteristic
200C22×C4×C61C2411yescharacteristic
201C2×C22⋊D61—24no—
202C2×C22⋊D61—24no—
203C2×C22⋊D61—24no—
204C2×C22⋊D61—42no—
205C2×C22⋊D61—42no—
206C2×C22⋊D61—42no—
207C2×C22⋊D61—42no—
208C2×C22⋊D61—42no—
209C2×C22⋊D61—42no—
210C22×Dic61—21no—
211C22×Dic61—22no—
212C22×Dic61—22no—
213C22×Dic61—22no—
214C22×Dic61—21no—
215C22×Dic61—21no—
216C22×Dic61C2×D411yescharacteristic
217C22×Dic61C2×D411yescharacteristic
218D4×D61—28no—
219D4×D61—28no—
220D4×D61—432no—
221D4×D61—44no—
222D4×D61—44no—
223C2×D244—21no—
224C2×D244—21no—
225C2×D244—21no—
226C2×D244—21no—
227C2×D244—24no—
228C2×D244—21no—
229C2×D244—42no—
230C2×D244—42no—
231C2×D244C2×D412yes—
232C2×C4×D61—22no—
233C2×C4×D61—24no—
234C2×C4×D61—22no—
235C2×C4×D61—22no—
236C2×C4×D61—21no—
237C2×C4×D61—21no—
238C2×C4×D61—21no—
239C2×C4×D61—21no—
240C2×C4×D61—21no—
241C2×C4×D61—21no—
242C2×C4×D61—22no—
243C2×C4×D61—22no—
244C2×C4×D61—22no—
245C2×C4×D61—42no—
246C2×C4×D61—42no—
247C2×C4×D61—44no—
248C2×C4×D61—44no—
249C2×C4×D61—44no—
250C2×C4×D61—44no—
251C2×C4×D61C2×D412yes—
252C2×C4×D61C2×D412yes—
253C2×C4×D61C2×D412yes—
254C2×C4×D61#4112yes—
255C2×C4×D61#4112yes—
256C2×C4×D61#4112yes—
257C2×C8×C61—21no—
258C2×C8×C61—21no—
259C2×C8×C61—21no—
260C2×C8×C61—21no—
261C2×C8×C61—21no—
262C2×C8×C61C2×D412yescomplemented
263C4⋊C4×C61—21no—
264C4⋊C4×C61—21no—
265C4⋊C4×C61—21no—
266C4⋊C4×C61—21no—
267C4⋊C4×C61—21no—
268C4⋊C4×C61C2×D412yes—
269C22⋊C4×C61—24no—
270C22⋊C4×C61—42no—
271C22⋊Dic61—24no—
272C22⋊Dic61—42no—
273#11758198—24no—
274#11758198—24no—
275#11758198—42no—
276#11758198—42no—
277#11758198—42no—
278#11758198—42no—
279C4⋊Dic61—21no—
280C4⋊Dic61—21no—
281C4⋊Dic61—21no—
282C4⋊Dic61—21no—
283C4⋊Dic61—21no—
284C4⋊Dic61C2×D412yes—
285#11758196—24no—
286C4×Dic61—42no—
287C4×Dic61—42no—
288C2×#92418—21no—
289C2×#92418—21no—
290C2×#92418—21no—
291C2×#92418—21no—
292C2×#92418—21no—
293C2×#92418C2×D412yescomplemented
294#11758189—28no—
295#11758189—44no—
296C23×C61—21no—
297C23×C61—21no—
298C23×C61—21no—
299C23×C61—21no—
300C23×C61—21no—
301C23×C61—21no—
302C23×C61—22no—
303C23×C61—41no—
304C23×C61—41no—
305C23×C61—41no—
306C23×C61—41no—
307C23×C61—41no—
308C23×C61—41no—
309C23×C61AGL(1,ℤ/8)12yes—
310C23×C61C22×D411yescharacteristic
311C22×D61—21no—
312C22×D61—21no—
313C22×D61—21no—
314C22×D61—21no—
315C22×D61—28no—
316C22×D61—21no—
317C22×D61—21no—
318C22×D61—21no—
319C22×D61—21no—
320C22×D61—21no—
321C22×D61—21no—
322C22×D61—22no—
323C22×D61—44no—
324C22×D61—44no—
325C22×D61—44no—
326C22×D61—44no—
327C22×D61—44no—
328C22×D61—48no—
329C22×D61—48no—
330C22×D61—44no—
331C22×D61—41no—
332C22×D61—41no—
333C22×D61—41no—
334C22×D61—41no—
335C22×D61—41no—
336C22×D61—41no—
337C22×D61—48no—
338C22×D61—84no—
339C22×D61—84no—
340C22×D61—84no—
341C22×D61—84no—
342C22×D61#12012yes—
343C22×D61#12112yes—
344C22×D61#12312yes—
345C22×D61AGL(1,ℤ/8)12yes—
346D4×C61—22no—
347D4×C61—22no—
348D4×C61—48no—
349D4×C61—41no—
350D4×C61—41no—
351C2×C4×C61—22no—
352C2×C4×C61—21no—
353C2×C4×C61—21no—
354C2×C4×C61—21no—
355C2×C4×C61—41no—
356C2×C4×C61—41no—
357C2×C4×C61—41no—
358C2×C4×C61—41no—
359C2×C4×C61—41no—
360C2×C4×C61—41no—
361C2×C4×C61—41no—
362C2×C4×C61—41no—
363C2×C4×C61—41no—
364C2×C4×C61—41no—
365C2×C4×C61—41no—
366C2×C4×C61—41no—
367C2×C4×C61C22×D411yescharacteristic
368C2×C4×C61C22×D411yescharacteristic
369C2×C4×C61C22×D411yescharacteristic
370C2×C4×C61C2×#4111yescharacteristic
371C2×C4×C61C2×#4111yescharacteristic
372C2×C4×C61C2×#4111yescharacteristic
373C22⋊D61—48no—
374C22⋊D61—48no—
375C22⋊D61—48no—
376C2×Dic61—22no—
377C2×Dic61—21no—
378C2×Dic61—21no—
379C2×Dic61—21no—
380C2×Dic61—41no—
381C2×Dic61—41no—
382C2×Dic61—44no—
383C2×Dic61—41no—
384C2×Dic61—41no—
385C2×Dic61—41no—
386C2×Dic61—41no—
387C2×Dic61—41no—
388C2×Dic61—41no—
389C2×Dic61#12012yes—
390C2×Dic61#12112yes—
391C2×Dic61#12312yes—
392D244—22no—
393D244—22no—
394D244—48no—
395D244—41no—
396D244—41no—
397C4×D61—48no—
398C4×D61—44no—
399C4×D61—41no—
400C4×D61—41no—
401C4×D61—41no—
402C4×D61—41no—
403C4×D61—44no—
404C4×D61#12114yes—
405C4×D61#12114yes—
406C4×D61#12314yes—
407C4×D61#12414yes—
408C8×C61—22no—
409C8×C61—41no—
410#92418—22no—
411#92418—41no—
412#23480—611nomaximal, Sylow
413C22×C61—22no—
414C22×C61—22no—
415C22×C61—22no—
416C22×C61—41no—
417C22×C61—41no—
418C22×C61—41no—
419C22×C61—41no—
420C22×C61—42no—
421C22×C61—42no—
422C22×C61—42no—
423C22×C61—81no—
424C22×C61—81no—
425C22×C61—81no—
426C22×C61—81no—
427C22×C61C2×#12011yescharacteristic
428C22×C61C2×#12111yescharacteristic
429C22×C61C2×#12311yescharacteristic
430C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
431C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
432C22×C61#57511yescharacteristic
433C22×C61#57511yescharacteristic
434C2×D61—22no—
435C2×D61—22no—
436C2×D61—22no—
437C2×D61—22no—
438C2×D61—22no—
439C2×D61—22no—
440C2×D61—22no—
441C2×D61—22no—
442C2×D61—22no—
443C2×D61—416no—
444C2×D61—41no—
445C2×D61—41no—
446C2×D61—41no—
447C2×D61—41no—
448C2×D61—42no—
449C2×D61—42no—
450C2×D61—42no—
451C2×D61—816no—
452C2×D61—81no—
453C2×D61—81no—
454C2×D61—81no—
455C2×D61—81no—
456C2×D61#39414yes—
457C4×C61—41no—
458C4×C61—42no—
459C4×C61—81no—
460C4×C61—81no—
461C4×C61C2×#12111yescharacteristic
462C4×C61C2×#12111yescharacteristic
463C4×C61C2×#12311yescharacteristic
464C4×C61C2×#12411yescharacteristic
465Dic61—41no—
466Dic61—42no—
467Dic61—81no—
468Dic61—81no—
469Dic61#39414yes—
470C22×#121—611no—
471C2×#428—611no—
472C2×#418—611no—
473C2×#418—611no—
474C2×#407—611no—
475#2280—611no—
476#2034—611no—
477#2034—611no—
478#2034—611no—
479#2034D6111yescharacteristic, complemented
480#2033—611no—
481#2033—611no—
482#2033—611no—
483#2033—611no—
484#1736—611no—
485C2×C61—42no—
486C2×C61—82no—
487C2×C61C2×#39411yescharacteristic
488C2×C61#300311yescharacteristic
489C2×C61#300511yescharacteristic
490C2×C61#305511yescharacteristic
491C2×C61#305511yescharacteristic
492C2×C61#309411yescharacteristic
493C2×C61#309411yescharacteristic
494D61—24no—
495D61—42no—
496D61—82no—
497C23×D4—611no—
498C23×D4—1221no—
499C24×C4—611no—
500C22×M16—611no—
501C22×M16—611no—
502C2×#121—611no—
503C2×#121—611no—
504C2×#121—611no—
505C2×#121—1221no—
506C2×#121—1224no—
507C2×#121—1224no—
508C2×#121—1221no—
509C2×#121C2×D6111yescharacteristic
510C2×#117—611no—
511C2×#117—611no—
512C22×C4⋊C4—611no—
513C22×C22⋊C4—1221no—
514#428—1224no—
515C2×#107—611no—
516C2×#107—611no—
517C2×#106—611no—
518C2×#106C2×D6111yescharacteristic, complemented
519#418—1224no—
520#418—1224no—
521C2×#102—611no—
522C2×#102—611no—
523C2×#102—611no—
524C2×#102—611no—
525C2×#102—611no—
526C2×#102—611no—
527C2×#102C2×D6111yescharacteristic, complemented
528C2×#102C2×D6111yescharacteristic, complemented
529#407—1224no—
530C2×C22⋊C8—611no—
531C2×C22⋊C8—611no—
532C2×C22⋊C8—611no—
533C2×C22⋊C8C2×D6111yescharacteristic, complemented
534#381—1221no—
535#380—611no—
536#380—611no—
537#380—611no—
538#380C2×D6111yescharacteristic, complemented
539#379—1221no—
540C4×C22⋊C4—1221no—
541C4×C22⋊C4—1221no—
542#340—611no—
543#340—611no—
544#340—611no—
545#340C2×D6111yescharacteristic, complemented
546C61#2348011yescharacteristic, complemented, Sylow
547C25—611no—
548C25—1221no—
549C22×D4—21no—
550C22×D4—614no—
551C22×D4—611no—
552C22×D4—1221no—
553C22×D4—1222no—
554C22×D4—1222no—
555C22×D4—1222no—
556C22×D4—1222no—
557C22×D4—1222no—
558C22×D4—1221no—
559C22×D4—1228no—
560C22×D4—1221no—
561C22×D4—1221no—
562C22×D4—2444no—
563C22×D4—2444no—
564C22×D4C22×D6111yescharacteristic
565C23×C4—611no—
566C23×C4—611no—
567C23×C4—611no—
568C23×C4—611no—
569C23×C4—611no—
570C23×C4—1222no—
571C23×C4—1222no—
572C23×C4—1222no—
573C23×C4—1222no—
574C23×C4—1222no—
575C23×C4—1222no—
576C23×C4—1221no—
577C23×C4C22×D6111yescharacteristic
578C2×M16—614no—
579C2×M16—1222no—
580C2×M16—1222no—
581C2×M16—1222no—
582C2×M16—1222no—
583C2×M16—1222no—
584C22×C8—611no—
585C22×C8—611no—
586C22×C8C22×D6111yescharacteristic
587C22×C8C22×D6111yescharacteristic
588#121—22no—
589#121—22no—
590#121—1228no—
591#121—1222no—
592#121—1222no—
593#121—1222no—
594#121—1222no—
595#121—1228no—
596#121—1222no—
597#121—1222no—
598#117—1222no—
599#117—1222no—
600#117—1222no—
601#117—1222no—
602C2×C4⋊C4—611no—
603C2×C4⋊C4—614no—
604C2×C4⋊C4—611no—
605C2×C4⋊C4—611no—
606C2×C4⋊C4—1222no—
607C2×C4⋊C4—1221no—
608C2×C4⋊C4C22×D6111yescharacteristic
609C2×C4⋊C4C22×D6111yescharacteristic
610C2×C4⋊C4C22×D6111yescharacteristic
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—1228no—
614C2×C22⋊C4—1221no—
615C2×C22⋊C4—1221no—
616C2×C22⋊C4—1221no—
617C2×C22⋊C4—1221no—
618C2×C22⋊C4—1221no—
619C2×C22⋊C4—1221no—
620C2×C22⋊C4—1221no—
621C2×C22⋊C4—1221no—
622C2×C42—1221no—
623C2×C42—1221no—
624#107—1222no—
625#107—1222no—
626#106—22no—
627#106—1222no—
628#102—22no—
629#102—22no—
630#102—1222no—
631#102—1222no—
632#102—1222no—
633#102—1222no—
634#102—1222no—
635#102—1222no—
636C22⋊C8—22no—
637C22⋊C8—1222no—
638C22⋊C8—1222no—
639C22⋊C8—1222no—
640#95—21no—
641#95—1221no—
642#95—1221no—
643#95—1221no—
644C24—21no—
645C24—611no—
646C24—611no—
647C24—1222no—
648C24—1222no—
649C24—1224no—
650C24—1222no—
651C24—1222no—
652C24—1222no—
653C24—1221no—
654C24—2441no—
655C24—2441no—
656C24—2442no—
657C24—2442no—
658C24—2442no—
659C24—2442no—
660C24—2442no—
661C24—2442no—
662C24D4×D6111yescharacteristic
663C2×D4—24no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—612no—
672C2×D4—1224no—
673C2×D4—1228no—
674C2×D4—1228no—
675C2×D4—1224no—
676C2×D4—1224no—
677C2×D4—1224no—
678C2×D4—1221no—
679C2×D4—1221no—
680C2×D4—1221no—
681C2×D4—1221no—
682C2×D4—1221no—
683C2×D4—2442no—
684C2×D4—2442no—
685C2×D4—2444no—
686C2×D4—2444no—
687C2×D4—2442no—
688C2×D4—2442no—
689C2×D4—24432no—
690C2×D4—2442no—
691C2×D4—2442no—
692C2×D4—2442no—
693C2×D4—2442no—
694C2×D4D4×D6112yes—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—611no—
705C22×C4—612no—
706C22×C4—612no—
707C22×C4—612no—
708C22×C4—612no—
709C22×C4—612no—
710C22×C4—612no—
711C22×C4—611no—
712C22×C4—1222no—
713C22×C4—1222no—
714C22×C4—1222no—
715C22×C4—1222no—
716C22×C4—1224no—
717C22×C4—1222no—
718C22×C4—1222no—
719C22×C4—1222no—
720C22×C4—1222no—
721C22×C4—1222no—
722C22×C4—1221no—
723C22×C4—1221no—
724C22×C4—1221no—
725C22×C4—1221no—
726C22×C4—1221no—
727C22×C4—1221no—
728C22×C4—1221no—
729C22×C4—1221no—
730C22×C4—1221no—
731C22×C4—2444no—
732C22×C4—2444no—
733C22×C4—2444no—
734C22×C4—2444no—
735C22×C4—2442no—
736C22×C4—2442no—
737C22×C4D4×D6111yescharacteristic
738C22×C4C23×D6111yescharacteristic
739M16—1228no—
740M16—2444no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—612no—
747C2×C8—1221no—
748C2×C8—1221no—
749C2×C8—1221no—
750C2×C8—1221no—
751C2×C8—1221no—
752C2×C8D4×D6112yescomplemented
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—612no—
759C4⋊C4—1224no—
760C4⋊C4—1221no—
761C4⋊C4—1221no—
762C4⋊C4—1221no—
763C4⋊C4—1221no—
764C4⋊C4—1221no—
765C4⋊C4D4×D6112yes—
766C22⋊C4—24no—
767C22⋊C4—42no—
768C22⋊C4—1224no—
769C22⋊C4—1224no—
770C22⋊C4—1224no—
771C22⋊C4—2442no—
772C22⋊C4—2442no—
773C22⋊C4—2442no—
774C22⋊C4—2442no—
775C22⋊C4—2442no—
776C42—2442no—
777C42—2442no—
778C23—21no—
779C23—21no—
780C23—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—22no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—612no—
792C23—612no—
793C23—612no—
794C23—612no—
795C23—1228no—
796C23—1221no—
797C23—1221no—
798C23—1221no—
799C23—1221no—
800C23—1221no—
801C23—1221no—
802C23—1221no—
803C23—1221no—
804C23—1221no—
805C23—1221no—
806C23—1222no—
807C23—4884no—
808C23—4884no—
809C23—4884no—
810C23—4884no—
811C23—2444no—
812C23—2444no—
813C23—2448no—
814C23—2444no—
815C23—2444no—
816C23—2444no—
817C23—2448no—
818C23—2448no—
819C23—2444no—
820C23—2441no—
821C23—2441no—
822C23—2441no—
823C23—2441no—
824C23—2441no—
825C23—2441no—
826C23#1451980412yes—
827C23C2×D4×D6111yescharacteristic
828D4—22no—
829D4—22no—
830D4—48no—
831D4—41no—
832D4—41no—
833D4—1222no—
834D4—1222no—
835D4—2448no—
836D4—2448no—
837D4—2448no—
838D4—2448no—
839D4—2441no—
840D4—2441no—
841C2×C4—21no—
842C2×C4—22no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—612no—
858C2×C4—612no—
859C2×C4—612no—
860C2×C4—614no—
861C2×C4—614no—
862C2×C4—614no—
863C2×C4—614no—
864C2×C4—1221no—
865C2×C4—1222no—
866C2×C4—1221no—
867C2×C4—1221no—
868C2×C4—2444no—
869C2×C4—2444no—
870C2×C4—2448no—
871C2×C4—2444no—
872C2×C4—2441no—
873C2×C4—2441no—
874C2×C4—2441no—
875C2×C4—2441no—
876C2×C4—2441no—
877C2×C4—2441no—
878C2×C4—2441no—
879C2×C4—2441no—
880C2×C4—2441no—
881C2×C4—2441no—
882C2×C4—2441no—
883C2×C4—2441no—
884C2×C4C2×D4×D6111yescharacteristic
885C2×C4C2×D4×D6111yescharacteristic
886C2×C4C2×D4×D6111yescharacteristic
887C2×C4#41×D6111yescharacteristic
888C2×C4#41×D6111yescharacteristic
889C2×C4#41×D6111yescharacteristic
890C8—22no—
891C8—41no—
892C8—1222no—
893C8—2441no—
894C22—22no—
895C22—22no—
896C22—22no—
897C22—41no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—81no—
905C22—81no—
906C22—81no—
907C22—81no—
908C22—614no—
909C22—1222no—
910C22—1222no—
911C22—1222no—
912C22—1222no—
913C22—1222no—
914C22—1222no—
915C22—1222no—
916C22—1222no—
917C22—1222no—
918C22—48816no—
919C22—4881no—
920C22—4881no—
921C22—4881no—
922C22—4881no—
923C22—24416no—
924C22—2442no—
925C22—2442no—
926C22—2442no—
927C22—2441no—
928C22—2441no—
929C22—2441no—
930C22—2441no—
931C22#120×D6111yescharacteristic
932C22#121×D6111yescharacteristic
933C22#123×D6111yescharacteristic
934C22AGL(1,ℤ/8)×D6111yescharacteristic
935C22C2×#1451980411yescharacteristic
936C22#1684055811yescharacteristic
937C22#1684055911yescharacteristic
938C4—41no—
939C4—42no—
940C4—81no—
941C4—81no—
942C4—614no—
943C4—4881no—
944C4—4881no—
945C4—2441no—
946C4—2442no—
947C4#121×D6111yescharacteristic
948C4#121×D6111yescharacteristic
949C4#123×D6111yescharacteristic
950C4#124×D6111yescharacteristic
951C2—42no—
952C2—82no—
953C2—1224no—
954C2—4882no—
955C2—2442no—
956C2#394×D6111yescharacteristic
957C2#2145504711yescharacteristic
958C2#2145505711yescharacteristic
959C2#2145543111yescharacteristic
960C2#2145543711yescharacteristic
961C2#2145575611yescharacteristic
962C2#2145575811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2034C2
socleC23×C61C22×D4
prime radicalC2×#121×D61C2
hypercenter#2034D61
hypocenterC61#23480
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2034

Complements

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

NH ≅ G/Ntype
2. C2×#16839801C2semidirect
3. C2×#16839765C2semidirect
4. C2×#16839765C2semidirect
5. C2×#16839724C2semidirect
6. #21448201C2semidirect
7. #21447010C2semidirect
8. #21447008C2semidirect
9. #21447006C2semidirect
10. #21447004C2semidirect
11. #21447002C2semidirect
12. #21447000C2semidirect
13. #21446998C2semidirect
14. #21445537C2semidirect
15. C61×#2034C2semidirect
33. C2×#14519711C22semidirect
34. C2×#14519710C22semidirect
35. C2×#14519708C22semidirect
38. C2×#14519699C22semidirect
39. C2×#14519699C22semidirect
40. C2×#14519698C22semidirect
41. C2×#14519698C22semidirect
42. C2×#14519697C22semidirect
43. C2×#14519697C22semidirect
45. C2×C22⋊#92418C22semidirect
46. C2×#14519689C22semidirect
47. C2×#14519689C22semidirect
49. #16839622C22semidirect
50. #16839619C22semidirect
51. #16839619C22semidirect
55. #16839525C22semidirect
56. #16839524C22semidirect
57. #16839524C22semidirect
59. C2×#106×C61C22semidirect
60. C2×#102×C61C22semidirect
61. C2×#102×C61C22semidirect
62. C2×C22⋊C8×C61C22semidirect
63. C61×#380C22semidirect
64. C61×#340C22semidirect
98. C2×#11758189D4semidirect
262. C2×C8×C61C2×D4semidirect
293. C2×#92418C2×D4semidirect
479. #2034D61semidirect
518. C2×#106C2×D61semidirect
527. C2×#102C2×D61semidirect
528. C2×#102C2×D61semidirect
533. C2×C22⋊C8C2×D61semidirect
538. #380C2×D61semidirect
545. #340C2×D61semidirect
546. C61#23480semidirect
752. C2×C8D4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#121×D612
C2×#168398012
C2×#168397652
C2×#168397242
#214482012
#214470102
#214470082
#214470062
#214470042
#214470022
#214470002
#214469982
#214455372
C61×#20342
#2348061