Finite Group Databasebeta

← #29681433

Subgroups — #29681433

Order 15616.

1926 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519804C211yesmaximal, characteristic
2C2×#16840244C211yesmaximal, characteristic, complemented
3C2×#16839757C211yesmaximal, characteristic, complemented
4C2×#102×D61C211yesmaximal, characteristic, complemented
5#21448398C211yesmaximal, characteristic, complemented
6#21446176C211yesmaximal, characteristic, complemented
7#21446174C211yesmaximal, characteristic, complemented
8#21446172C211yesmaximal, characteristic, complemented
9#21446170C211yesmaximal, characteristic, complemented
10#21446168C211yesmaximal, characteristic, complemented
11#21446166C211yesmaximal, characteristic, complemented
12#21446164C211yesmaximal, characteristic, complemented
13#21445537C211yesmaximal, characteristic, complemented
14#21445514C211yesmaximal, characteristic, complemented
15C61×#1880C211yesmaximal, characteristic, complemented
16C22×#11758226C2211yescharacteristic
17C22×D4×D61C2211yescharacteristic
18C2×#14519804—24no—
19C2×#14519804—24no—
20C2×#14519804C418yescomplemented
21C22×#11758201C2211yescharacteristic
22C22×D488C2211yescharacteristic
23C22×#11758199C2211yescharacteristic
24C22×#11758189C2211yescharacteristic
25C22×C8×D61C2211yescharacteristic
26#16840244—24no—
27#16840244—24no—
28C2×Q8×Dic61C2211yescharacteristic, complemented
29C2×C4×D244—21no—
30C2×C4×D244C2211yescharacteristic, complemented
31C2×#14519739—21no—
32C2×#14519739C2211yescharacteristic, complemented
33C2×#14519735C2211yescharacteristic
34C2×#14519734—21no—
35C2×#14519734C2211yescharacteristic
36C2×C4⋊C4×D61—21no—
37C2×C4⋊C4×D61C2211yescharacteristic
38#16839757—24no—
39C2×#14519701C2211yescharacteristic, complemented
40C2×#14519699C2211yescharacteristic
41C2×#14519699C2211yescharacteristic, complemented
42C2×#14519698C2211yescharacteristic
43C2×#14519697C2211yescharacteristic
44C2×#14519697C2211yescharacteristic, complemented
45#102×D61—24no—
46#16839665C2211yescharacteristic
47#16839664C2211yescharacteristic
48#16839663C2211yescharacteristic
49#16839662—21no—
50#16839662—21no—
51#16839617—21no—
52#16839617—21no—
53#16839525C2211yescharacteristic, complemented
54#16839524C2211yescharacteristic, complemented
55#16839524C2211yescharacteristic, complemented
56#16839517C2211yescharacteristic, complemented
57#16839516C2211yescharacteristic, complemented
58#16839516C2211yescharacteristic, complemented
59C22×SD16×C61C2211yescharacteristic
60C2×C4×Q8×C61C2211yescharacteristic, complemented
61C2×#103×C61C2211yescharacteristic, complemented
62C2×#102×C61C2211yescharacteristic
63C61×#390C2211yescharacteristic
64C61×#340C2211yescharacteristic, complemented
65C61×#336C2211yescharacteristic, complemented
66C24×D61—21no—
67C2×#11758226—22no—
68C2×#11758226—22no—
69C2×#11758226—22no—
70C2×#11758226C2×C414yes—
71C2×#11758226D414yes—
72C2×#11758226D414yes—
73C22×D244—21no—
74C22×D244C2311yescharacteristic
75C22×D244C2311yescharacteristic
76C22×C22⋊D61—21no—
77C2×D4×D61—22no—
78C2×D4×D61—22no—
79C2×D4×D61—22no—
80C2×D4×D61—22no—
81C2×D4×D61—22no—
82C2×D4×D61C2×C414yescomplemented
83C22×C4×D61—21no—
84C22×C4×D61—21no—
85C22×C4×D61—21no—
86C22×C4×D61—21no—
87C22×C4×D61C2311yescharacteristic
88#14519804—232no—
89C2×#11758201—22no—
90C2×#11758201—22no—
91C2×#11758201C2×C414yescomplemented
92C2×D488—22no—
93C2×D488—22no—
94C2×D488C2×C414yescomplemented
95C2×#11758199—22no—
96C2×#11758199—22no—
97C2×#11758199C2×C414yescomplemented
98C2×#11758189—22no—
99C2×#11758189—22no—
100C2×#11758189C2×C414yescomplemented
101C22×#92418C2311yescharacteristic
102C22×#92418C2311yescharacteristic
103C2×C8×D61—22no—
104C2×C8×D61—22no—
105C2×C8×D61—22no—
106Q8×Dic61—22no—
107Q8×Dic61—22no—
108C4×D244—28no—
109C4×D244—22no—
110C4×D244—22no—
111#14519739—28no—
112#14519739—22no—
113#14519739—22no—
114#14519735—22no—
115#14519735—22no—
116#14519734—28no—
117#14519734—22no—
118#14519734—22no—
119C2×C4⋊Dic61—21no—
120C2×C4⋊Dic61C2311yescharacteristic
121C2×C4⋊Dic61C2311yescharacteristic
122C2×#11758196—21no—
123C2×#11758196D411yescharacteristic
124C2×#11758196D411yescharacteristic
125C4⋊C4×D61—28no—
126C4⋊C4×D61—22no—
127C4⋊C4×D61D414yes—
128C2×C22⋊Dic61—21no—
129C2×C22⋊Dic61—21no—
130C2×#11758198—21no—
131C2×#11758198—21no—
132C2×#11758198—21no—
133C2×#11758198—21no—
134C2×#11758198—21no—
135C2×#11758198—21no—
136C2×#11758198—21no—
137C2×#11758198D411yescharacteristic
138C2×#11758198D411yescharacteristic
139C2×C4×Dic61—21no—
140C2×C4×Dic61—21no—
141C2×C4×Dic61C2311yescharacteristic
142#14519701—22no—
143#14519699—22no—
144#14519699—22no—
145#14519698—22no—
146#14519697—22no—
147#14519697—22no—
148C22×Q8×C61C2311yescharacteristic
149C22×D4×C61C2311yescharacteristic
150C2×SD16×C61—22no—
151C2×SD16×C61—22no—
152C2×SD16×C61C2×C414yescomplemented
153C22×C8×C61C2311yescharacteristic
154C22×C8×C61C2311yescharacteristic
155C4×Q8×C61—22no—
156C4×Q8×C61—22no—
157C2×C4⋊C4×C61—21no—
158C2×C4⋊C4×C61C2311yescharacteristic
159C2×C4⋊C4×C61C2311yescharacteristic
160C2×C22⋊C4×C61—21no—
161C2×C22⋊C4×C61—21no—
162C2×C42×C61—21no—
163C2×C42×C61C2311yescharacteristic
164#103×C61—22no—
165#102×C61—22no—
166C24×C61—21no—
167C23×D61—21no—
168C23×D61—21no—
169C23×D61—24no—
170C23×D61—42no—
171C23×D61—42no—
172C23×D61—81no—
173C23×D61—81no—
174C23×D61—81no—
175C23×D61—81no—
176C23×D61C2×D411yescharacteristic
177C2×Q8×C61—21no—
178C2×Q8×C61—21no—
179C2×Q8×C61—21no—
180C2×Q8×C61C22×C412yes—
181C2×Q8×C61C2×D412yes—
182C2×Q8×C61C2×D412yes—
183C2×D4×C61—21no—
184C2×D4×C61—21no—
185C2×D4×C61—21no—
186C2×D4×C61—21no—
187C2×D4×C61—21no—
188C2×D4×C61C22×C412yes—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61C2×D411yescharacteristic
193C22×C4×C61C2×D411yescharacteristic
194C22×C4×C61C2411yescharacteristic
195C2×C22⋊D61—24no—
196C2×C22⋊D61—42no—
197C2×C22⋊D61—42no—
198C22×Dic61—21no—
199C22×Dic61—21no—
200C22×Dic61C2×D411yescharacteristic
201C22×Dic61C2×D411yescharacteristic
202C22×Dic61C2×D411yescharacteristic
203#11758226—28no—
204#11758226—28no—
205#11758226—28no—
206#11758226C22⋊C4116yescomplemented
207D4×D61—28no—
208D4×D61—28no—
209D4×D61—44no—
210D4×D61—44no—
211C2×D244—24no—
212C2×D244—24no—
213C2×D244—24no—
214C2×D244—21no—
215C2×D244—21no—
216C2×D244—21no—
217C2×D244—21no—
218C2×D244—21no—
219C2×D244—21no—
220C2×D244—21no—
221C2×D244—21no—
222C2×D244C22×C412yes—
223C2×D244C22×C412yes—
224C2×D244C2×D412yes—
225C2×D244C2×D412yes—
226C2×C4×D61—24no—
227C2×C4×D61—24no—
228C2×C4×D61—24no—
229C2×C4×D61—24no—
230C2×C4×D61—24no—
231C2×C4×D61—24no—
232C2×C4×D61—81no—
233C2×C4×D61—81no—
234C2×C4×D61—81no—
235C2×C4×D61—81no—
236C2×C4×D61—81no—
237C2×C4×D61—81no—
238C2×C4×D61C22×C412yes—
239C2×C4×D61C2×D412yes—
240C2×C4×D61C2×D412yes—
241C2×C4×D61C2×D412yes—
242C2×C4×D61#4112yes—
243C2×C4×D61#4112yes—
244SD16×C61—28no—
245C2×C8×C61—21no—
246C2×C8×C61—21no—
247C2×C8×C61—21no—
248C2×C8×C61—21no—
249C2×C8×C61—21no—
250C2×C8×C61C22×C412yes—
251C4⋊C4×C61—24no—
252C4⋊C4×C61—21no—
253C4⋊C4×C61—21no—
254C4⋊C4×C61—21no—
255C4⋊C4×C61C2×D412yes—
256C22⋊C4×C61—81no—
257C22⋊C4×C61—81no—
258C42×C61—24no—
259C42×C61—21no—
260C42×C61—21no—
261C22⋊Dic61—81no—
262C22⋊Dic61—81no—
263#11758201—28no—
264#11758199—28no—
265#11758198—24no—
266#11758198—24no—
267#11758198—22no—
268#11758198—22no—
269#11758198—42no—
270#11758198—81no—
271#11758198—81no—
272#11758198—81no—
273#11758198—81no—
274C4⋊Dic61—24no—
275C4⋊Dic61—21no—
276C4⋊Dic61—21no—
277C4⋊Dic61—21no—
278C4⋊Dic61C2×D412yes—
279#11758196—22no—
280#11758196—24no—
281#11758196—22no—
282C4×Dic61—24no—
283C4×Dic61—21no—
284C4×Dic61—21no—
285C4×Dic61—42no—
286C2×#92418—21no—
287C2×#92418—21no—
288C2×#92418—21no—
289C2×#92418—21no—
290C2×#92418—21no—
291C2×#92418C22×C412yes—
292D488—28no—
293#11758189—28no—
294C8×D61—44no—
295C23×C61—22no—
296C23×C61—41no—
297C23×C61—41no—
298C23×C61—41no—
299C23×C61—41no—
300C23×C61—41no—
301C23×C61—41no—
302C23×C61C22×D411yescharacteristic
303C22×D61—21no—
304C22×D61—21no—
305C22×D61—21no—
306C22×D61—21no—
307C22×D61—22no—
308C22×D61—22no—
309C22×D61—22no—
310C22×D61—22no—
311C22×D61—41no—
312C22×D61—41no—
313C22×D61—41no—
314C22×D61—41no—
315C22×D61—41no—
316C22×D61—41no—
317C22×D61—41no—
318C22×D61—41no—
319C22×D61—41no—
320C22×D61—41no—
321C22×D61—48no—
322C22×D61—84no—
323C22×D61—84no—
324C22×D61—84no—
325C22×D61—84no—
326C22×D61—84no—
327C22×D61—84no—
328C22×D61C4×D412yes—
329C22×D61#12012yes—
330C22×D61#12112yes—
331Q8×C61—22no—
332Q8×C61—22no—
333Q8×C61—22no—
334Q8×C61C2×C22⋊C414yes—
335D4×C61—22no—
336D4×C61—22no—
337D4×C61—41no—
338D4×C61—41no—
339C2×C4×C61—22no—
340C2×C4×C61—22no—
341C2×C4×C61—22no—
342C2×C4×C61—21no—
343C2×C4×C61—21no—
344C2×C4×C61—22no—
345C2×C4×C61—21no—
346C2×C4×C61—21no—
347C2×C4×C61—21no—
348C2×C4×C61—21no—
349C2×C4×C61—41no—
350C2×C4×C61—41no—
351C2×C4×C61—41no—
352C2×C4×C61—41no—
353C2×C4×C61—41no—
354C2×C4×C61C23×C411yescharacteristic
355C2×C4×C61C22×D411yescharacteristic
356C2×C4×C61C22×D411yescharacteristic
357C2×C4×C61C22×D411yescharacteristic
358C2×C4×C61C2×#4111yescharacteristic
359C2×C4×C61C2×#4111yescharacteristic
360C22⋊D61—48no—
361C2×Dic61—21no—
362C2×Dic61—21no—
363C2×Dic61—22no—
364C2×Dic61—21no—
365C2×Dic61—21no—
366C2×Dic61—21no—
367C2×Dic61—21no—
368C2×Dic61—41no—
369C2×Dic61—41no—
370C2×Dic61—41no—
371C2×Dic61—41no—
372C2×Dic61—41no—
373C2×Dic61C4×D412yes—
374C2×Dic61#12012yes—
375C2×Dic61#12112yes—
376D244—216no—
377D244—22no—
378D244—22no—
379D244—22no—
380D244—22no—
381D244—22no—
382D244—41no—
383D244—41no—
384D244C2×C22⋊C414yes—
385C4×D61—216no—
386C4×D61—84no—
387C4×D61—84no—
388C4×D61—84no—
389C4×D61C2×C22⋊C414yes—
390C4×D61C4×D414yes—
391C4×D61#12114yes—
392C4×D61#12314yes—
393C8×C61—22no—
394C8×C61—41no—
395#92418—22no—
396#92418—41no—
397#20932—611nomaximal, Sylow
398C22×C61—42no—
399C22×C61—42no—
400C22×C61—42no—
401C22×C61—81no—
402C22×C61—81no—
403C22×C61—81no—
404C22×C61—81no—
405C22×C61C2×C4×D411yescharacteristic
406C22×C61C2×#12011yescharacteristic
407C22×C61C2×#12111yescharacteristic
408C22×C61#57611yescharacteristic
409C22×C61#57611yescharacteristic
410C22×C61#57711yescharacteristic
411C22×C61#57711yescharacteristic
412C2×D61—22no—
413C2×D61—22no—
414C2×D61—22no—
415C2×D61—22no—
416C2×D61—22no—
417C2×D61—22no—
418C2×D61—24no—
419C2×D61—42no—
420C2×D61—42no—
421C2×D61—42no—
422C2×D61—42no—
423C2×D61—42no—
424C2×D61—42no—
425C2×D61—42no—
426C2×D61—42no—
427C2×D61—42no—
428C2×D61—816no—
429C2×D61—81no—
430C2×D61—81no—
431C2×D61—81no—
432C2×D61—81no—
433C2×D61#38614yes—
434C4×C61—24no—
435C4×C61—41no—
436C4×C61—42no—
437C4×C61—41no—
438C4×C61—81no—
439C4×C61C22×C22⋊C411yescharacteristic
440C4×C61C2×C4×D411yescharacteristic
441C4×C61C2×#12111yescharacteristic
442C4×C61C2×#12311yescharacteristic
443Dic61—41no—
444Dic61—42no—
445Dic61—41no—
446Dic61—81no—
447Dic61#38614yes—
448C22×AGL(1,ℤ/8)—611no—
449C2×#520—611no—
450C2×#416—611no—
451C22×#102—611no—
452#2309—611no—
453#1880—611no—
454#1880—611no—
455#1880—611no—
456#1880D6111yescharacteristic, complemented
457#1879—611no—
458#1879—611no—
459#1879—611no—
460#1879—611no—
461#1736—611no—
462#1729—611no—
463C2×C61—82no—
464C2×C61C2×#38611yescharacteristic
465C2×C61#294611yescharacteristic
466C2×C61#294611yescharacteristic
467C2×C61#300811yescharacteristic
468C2×C61#301011yescharacteristic
469C2×C61#304511yescharacteristic
470C2×C61#304511yescharacteristic
471D61—24no—
472D61—44no—
473D61—82no—
474C22×#41—611no—
475C23×D4—611no—
476C2×AGL(1,ℤ/8)—618no—
477C2×AGL(1,ℤ/8)—1224no—
478C2×AGL(1,ℤ/8)—1224no—
479C22×SD16—611no—
480C22×SD16C2×D6111yescharacteristic
481C22×D8—611no—
482C22×D8—611no—
483C22×M16—611no—
484C23×C8—611no—
485#520—1224no—
486#520—1224no—
487C2×C4×Q8—611no—
488C2×C4×Q8C2×D6111yescharacteristic, complemented
489C2×C4×D4—611no—
490C2×C4×D4—611no—
491C2×C4×D4—1221no—
492C2×C4×D4—1221no—
493C2×#117—611no—
494C2×#117—611no—
495C2×#117—1221no—
496C22×C4⋊C4—611no—
497C22×C4⋊C4—1221no—
498#416—1224no—
499C2×#103—611no—
500C2×#103C2×D6111yescharacteristic, complemented
501C2×#102—611no—
502C2×#102—611no—
503C2×#102—611no—
504C2×#102—611no—
505C2×#102—611no—
506C2×#102—1224no—
507C2×#102C2×D6111yescharacteristic
508#390—611no—
509#390—611no—
510#390—611no—
511#390—1221no—
512#390—1221no—
513#390C2×D6111yescharacteristic
514#379—1221no—
515#379—1221no—
516#340—611no—
517#340—611no—
518#340—611no—
519#340C2×D6111yescharacteristic, complemented
520#336—611no—
521#336—611no—
522#336—611no—
523#336C2×D6111yescharacteristic, complemented
524C61#2093211yescharacteristic, complemented, Sylow
525C25—1221no—
526C2×#41—614no—
527C2×#41—614no—
528C2×#41—614no—
529C2×#41—1222no—
530C2×#41—1222no—
531C2×#41—1222no—
532C22×Q8C22×D6111yescharacteristic
533C22×D4—614no—
534C22×D4—611no—
535C22×D4—611no—
536C22×D4—1221no—
537C22×D4—1222no—
538C22×D4—1222no—
539C22×D4—1222no—
540C22×D4—1222no—
541C22×D4—1222no—
542C22×D4—1221no—
543C22×D4C22×D6111yescharacteristic
544C23×C4—611no—
545C23×C4—1221no—
546C23×C4—1221no—
547C23×C4—1221no—
548C23×C4—1221no—
549AGL(1,ℤ/8)—12232no—
550C2×SD16—22no—
551C2×SD16—22no—
552C2×SD16—614no—
553C2×SD16—1222no—
554C2×SD16—1222no—
555C2×SD16C4×D6114yescomplemented
556C2×D8—614no—
557C2×D8—614no—
558C2×D8—1222no—
559C2×D8—1222no—
560C2×D8—1222no—
561C2×D8—1222no—
562C2×M16—614no—
563C2×M16—1222no—
564C2×M16—1222no—
565C22×C8—611no—
566C22×C8—611no—
567C22×C8—1222no—
568C22×C8—1222no—
569C22×C8—1222no—
570C22×C8C22×D6111yescharacteristic
571C22×C8C22×D6111yescharacteristic
572C4×Q8—22no—
573C4×Q8—22no—
574C4×Q8—1222no—
575C4×Q8—1222no—
576C4×D4—1222no—
577C4×D4—1222no—
578C4×D4—1228no—
579C4×D4—1222no—
580C4×D4—1228no—
581C4×D4—1222no—
582#117—1222no—
583#117—1222no—
584#117—1228no—
585#117—1222no—
586#117—1222no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—611no—
589C2×C4⋊C4—614no—
590C2×C4⋊C4—611no—
591C2×C4⋊C4—611no—
592C2×C4⋊C4—611no—
593C2×C4⋊C4—1222no—
594C2×C4⋊C4—1228no—
595C2×C4⋊C4—1221no—
596C2×C4⋊C4—1221no—
597C2×C4⋊C4C22×D6111yescharacteristic
598C2×C4⋊C4C22×D6111yescharacteristic
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—611no—
602C2×C22⋊C4—611no—
603C2×C22⋊C4—1221no—
604C2×C22⋊C4—1221no—
605C2×C22⋊C4—1221no—
606C2×C22⋊C4—1221no—
607C2×C22⋊C4—1221no—
608C2×C22⋊C4—1221no—
609C2×C22⋊C4—1221no—
610C2×C22⋊C4—1221no—
611C2×C22⋊C4—1221no—
612C2×C42—21no—
613C2×C42—611no—
614C2×C42—1221no—
615C2×C42—1221no—
616C2×C42C22×D6111yescharacteristic
617#103—22no—
618#103—1222no—
619#102—22no—
620#102—1222no—
621#102—1222no—
622#102—1222no—
623#102—1222no—
624#102—1222no—
625C24—21no—
626C24—611no—
627C24—1224no—
628C24—1221no—
629C24—1221no—
630C24—4881no—
631C24—4881no—
632C24—4881no—
633C24—4881no—
634C24—2442no—
635C24—2442no—
636#41—6116no—
637#41—1228no—
638#41—1228no—
639#41—1228no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8C2×C4×D6112yes—
644C2×Q8D4×D6112yes—
645C2×Q8D4×D6112yes—
646C2×D4—21no—
647C2×D4—21no—
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—21no—
651C2×D4—612no—
652C2×D4—612no—
653C2×D4—612no—
654C2×D4—612no—
655C2×D4—1224no—
656C2×D4—1224no—
657C2×D4—1224no—
658C2×D4—1228no—
659C2×D4—1228no—
660C2×D4—1224no—
661C2×D4—1221no—
662C2×D4—1221no—
663C2×D4—1221no—
664C2×D4—1221no—
665C2×D4—1221no—
666C2×D4—1221no—
667C2×D4—1221no—
668C2×D4—1221no—
669C2×D4—2444no—
670C2×D4—2444no—
671C2×D4—2442no—
672C2×D4—2442no—
673C2×D4C2×C4×D6112yes—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—611no—
678C22×C4—612no—
679C22×C4—612no—
680C22×C4—612no—
681C22×C4—612no—
682C22×C4—612no—
683C22×C4—612no—
684C22×C4—611no—
685C22×C4—611no—
686C22×C4—1224no—
687C22×C4—1224no—
688C22×C4—1224no—
689C22×C4—1224no—
690C22×C4—1224no—
691C22×C4—1224no—
692C22×C4—1221no—
693C22×C4—1221no—
694C22×C4—4881no—
695C22×C4—4881no—
696C22×C4—4881no—
697C22×C4—4881no—
698C22×C4—4881no—
699C22×C4—4881no—
700C22×C4D4×D6111yescharacteristic
701C22×C4D4×D6111yescharacteristic
702C22×C4C23×D6111yescharacteristic
703SD16—28no—
704SD16—1228no—
705D8—1228no—
706D8—1228no—
707M16—1228no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—612no—
714C2×C8—1221no—
715C2×C8—1221no—
716C2×C8—1221no—
717C2×C8—1221no—
718C2×C8—1221no—
719C2×C8—2444no—
720C2×C8C2×C4×D6112yes—
721C4⋊C4—24no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—612no—
726C4⋊C4—1222no—
727C4⋊C4—1224no—
728C4⋊C4—1222no—
729C4⋊C4—1224no—
730C4⋊C4—1221no—
731C4⋊C4—1221no—
732C4⋊C4—1221no—
733C4⋊C4D4×D6112yes—
734C22⋊C4—81no—
735C22⋊C4—81no—
736C22⋊C4—1222no—
737C22⋊C4—1222no—
738C22⋊C4—1224no—
739C22⋊C4—1224no—
740C22⋊C4—4881no—
741C22⋊C4—4881no—
742C22⋊C4—4881no—
743C22⋊C4—4881no—
744C22⋊C4—4881no—
745C22⋊C4—4881no—
746C22⋊C4—2442no—
747C42—24no—
748C42—21no—
749C42—21no—
750C42—1224no—
751C42—1221no—
752C42—1221no—
753C42—2442no—
754C23—22no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—612no—
762C23—612no—
763C23—612no—
764C23—1221no—
765C23—1221no—
766C23—1221no—
767C23—1221no—
768C23—1222no—
769C23—1222no—
770C23—1222no—
771C23—1222no—
772C23—4884no—
773C23—4884no—
774C23—4884no—
775C23—4884no—
776C23—4884no—
777C23—4884no—
778C23—2448no—
779C23—2441no—
780C23—2441no—
781C23—2441no—
782C23—2441no—
783C23—2441no—
784C23—2441no—
785C23—2441no—
786C23—2441no—
787C23—2441no—
788C23—2441no—
789C23C2×D4×D6111yescharacteristic
790Q8—22no—
791Q8—22no—
792Q8—22no—
793Q8C22⋊C4×D6114yes—
794D4—22no—
795D4—22no—
796D4—41no—
797D4—41no—
798D4—614no—
799D4—12216no—
800D4—1222no—
801D4—1222no—
802D4—1222no—
803D4—1222no—
804D4—1222no—
805D4—2448no—
806D4—2441no—
807D4—2441no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—22no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—612no—
824C2×C4—612no—
825C2×C4—612no—
826C2×C4—614no—
827C2×C4—614no—
828C2×C4—614no—
829C2×C4—614no—
830C2×C4—12216no—
831C2×C4—1221no—
832C2×C4—1222no—
833C2×C4—1221no—
834C2×C4—1221no—
835C2×C4—1221no—
836C2×C4—1221no—
837C2×C4—1221no—
838C2×C4—4884no—
839C2×C4—4884no—
840C2×C4—4884no—
841C2×C4—2441no—
842C2×C4—2441no—
843C2×C4—2441no—
844C2×C4—2441no—
845C2×C4—2441no—
846C2×C4C22×C4×D6111yescharacteristic
847C2×C4C2×D4×D6111yescharacteristic
848C2×C4C2×D4×D6111yescharacteristic
849C2×C4C2×D4×D6111yescharacteristic
850C2×C4#41×D6111yescharacteristic
851C2×C4#41×D6111yescharacteristic
852C8—22no—
853C8—41no—
854C8—1222no—
855C8—2441no—
856C22—42no—
857C22—42no—
858C22—42no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22—614no—
864C22—1222no—
865C22—1222no—
866C22—1222no—
867C22—1222no—
868C22—1222no—
869C22—1222no—
870C22—1224no—
871C22—48816no—
872C22—4881no—
873C22—4881no—
874C22—4881no—
875C22—4881no—
876C22—2442no—
877C22—2442no—
878C22—2442no—
879C22—2442no—
880C22—2442no—
881C22—2442no—
882C22—2442no—
883C22—2442no—
884C22—2442no—
885C22C4×D4×D6111yescharacteristic
886C22#120×D6111yescharacteristic
887C22#121×D6111yescharacteristic
888C22#1684056411yescharacteristic
889C22#1684056611yescharacteristic
890C22#1684056811yescharacteristic
891C22#1684057111yescharacteristic
892C4—24no—
893C4—41no—
894C4—42no—
895C4—41no—
896C4—81no—
897C4—614no—
898C4—4881no—
899C4—2441no—
900C4—2442no—
901C4—2441no—
902C4C2×C22⋊C4×D6111yescharacteristic
903C4C4×D4×D6111yescharacteristic
904C4#121×D6111yescharacteristic
905C4#123×D6111yescharacteristic
906C2—82no—
907C2—1224no—
908C2—4882no—
909C2—2444no—
910C2#386×D6111yescharacteristic
911C2#2145464611yescharacteristic
912C2#2145465011yescharacteristic
913C2#2145508411yescharacteristic
914C2#2145510011yescharacteristic
915C2#2145535511yescharacteristic
916C2#2145536111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1880C2
socleC23×C61C22×D4
prime radicalC22×#14519804C2
cosocleC22×C4×C61C24
hypercenter#1880D61
hypocenterC61#20932
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1880

Complements

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

NH ≅ G/Ntype
2. C2×#16840244C2semidirect
3. C2×#16839757C2semidirect
4. C2×#102×D61C2semidirect
5. #21448398C2semidirect
6. #21446176C2semidirect
7. #21446174C2semidirect
8. #21446172C2semidirect
9. #21446170C2semidirect
10. #21446168C2semidirect
11. #21446166C2semidirect
12. #21446164C2semidirect
13. #21445537C2semidirect
14. #21445514C2semidirect
15. C61×#1880C2semidirect
20. C2×#14519804C4semidirect
28. C2×Q8×Dic61C22semidirect
30. C2×C4×D244C22semidirect
32. C2×#14519739C22semidirect
39. C2×#14519701C22semidirect
41. C2×#14519699C22semidirect
44. C2×#14519697C22semidirect
53. #16839525C22semidirect
54. #16839524C22semidirect
55. #16839524C22semidirect
56. #16839517C22semidirect
57. #16839516C22semidirect
58. #16839516C22semidirect
60. C2×C4×Q8×C61C22semidirect
61. C2×#103×C61C22semidirect
64. C61×#340C22semidirect
65. C61×#336C22semidirect
82. C2×D4×D61C2×C4semidirect
91. C2×#11758201C2×C4semidirect
94. C2×D488C2×C4semidirect
97. C2×#11758199C2×C4semidirect
100. C2×#11758189C2×C4semidirect
152. C2×SD16×C61C2×C4semidirect
206. #11758226C22⋊C4semidirect
456. #1880D61semidirect
488. C2×C4×Q8C2×D61semidirect
500. C2×#103C2×D61semidirect
519. #340C2×D61semidirect
523. #336C2×D61semidirect
524. C61#20932semidirect
555. C2×SD16C4×D61semidirect

Maximal subgroups

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

subgroupindex
C22×#145198042
C2×#168402442
C2×#168397572
C2×#102×D612
#214483982
#214461762
#214461742
#214461722
#214461702
#214461682
#214461662
#214461642
#214455372
#214455142
C61×#18802
#2093261