Finite Group Databasebeta

← #29681440

Subgroups — #29681440

Order 15616.

1906 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
1C22×SD16×D61C211yesmaximal, characteristic
2C2×#16840234C211yesmaximal, characteristic
3C2×#16839769C211yesmaximal, characteristic, complemented
4C2×#16839765C211yesmaximal, characteristic
5#21448402C211yesmaximal, characteristic, complemented
6#21446156C211yesmaximal, characteristic, complemented
7#21446155C211yesmaximal, characteristic, complemented
8#21446154C211yesmaximal, characteristic, complemented
9#21446153C211yesmaximal, characteristic, complemented
10#21446152C211yesmaximal, characteristic, complemented
11#21446151C211yesmaximal, characteristic, complemented
12#21446150C211yesmaximal, characteristic, complemented
13#21445534C211yesmaximal, characteristic, complemented
14#21445514C211yesmaximal, characteristic, complemented
15C61×#1877C211yesmaximal, characteristic, complemented
16C22×Q8×D61C2211yescharacteristic
17C22×D4×D61C2211yescharacteristic
18C22×#11758190C2211yescharacteristic
19C22×#11758200C2211yescharacteristic
20C22×#11758201C2211yescharacteristic
21C2×SD16×D61—24no—
22C2×SD16×D61—24no—
23C2×SD16×D61C418yescomplemented
24C22×#11758189C2211yescharacteristic
25C22×C8×D61C2211yescharacteristic
26#16840234—24no—
27#16840234—24no—
28C2×C4×D244C2211yescharacteristic
29C2×D4×Dic61C2211yescharacteristic
30C2×#14519739C2211yescharacteristic
31C2×C4×C22⋊D61—21no—
32C2×#14519737—21no—
33C2×#14519735C2211yescharacteristic
34C2×#14519735C2211yescharacteristic
35C2×#14519734C2211yescharacteristic
36C22×#11758198—21no—
37C2×C22⋊C4×D61—21no—
38#16839769—24no—
39#16839765—24no—
40C2×#14519702C2211yescharacteristic, complemented
41C2×#14519701C2211yescharacteristic, complemented
42C2×#14519700C2211yescharacteristic, complemented
43C2×#14519699C2211yescharacteristic
44C2×#14519698C2211yescharacteristic
45C2×#14519697C2211yescharacteristic
46#16839669C2211yescharacteristic, complemented
47#16839668C2211yescharacteristic, complemented
48#16839667C2211yescharacteristic, complemented
49#16839666—21no—
50#16839666—21no—
51#16839624—21no—
52#16839624—21no—
53#16839525C2211yescharacteristic, complemented
54#16839524C2211yescharacteristic, complemented
55#16839524C2211yescharacteristic, complemented
56#16839517C2211yescharacteristic, complemented
57#16839516C2211yescharacteristic, complemented
58#16839516C2211yescharacteristic, complemented
59C22×SD16×C61C2211yescharacteristic
60C2×C4×D4×C61C2211yescharacteristic
61C2×#103×C61C2211yescharacteristic, complemented
62C2×#102×C61C2211yescharacteristic
63C61×#391C2211yescharacteristic, complemented
64C61×#340C2211yescharacteristic, complemented
65C61×#336C2211yescharacteristic, complemented
66C24×D61—21no—
67C22×Dic122—21no—
68C22×Dic122C2311yescharacteristic
69C2×Q8×D61—22no—
70C2×Q8×D61—22no—
71C2×Q8×D61—22no—
72C2×Q8×D61—22no—
73C2×Q8×D61—22no—
74C2×Q8×D61C2×C414yescomplemented
75C22×D244C2311yescharacteristic
76C22×C22⋊D61—21no—
77C2×D4×D61—22no—
78C2×D4×D61—22no—
79C2×D4×D61—22no—
80C2×D4×D61C2×C414yes—
81C2×D4×D61D414yes—
82C2×D4×D61D414yes—
83C23×Dic61—21no—
84C22×C4×D61—21no—
85C22×C4×D61—21no—
86C22×C4×D61—21no—
87C22×C4×D61C2311yescharacteristic
88C2×#11758190—22no—
89C2×#11758190—22no—
90C2×#11758190C2×C414yescomplemented
91C2×#11758200—22no—
92C2×#11758200—22no—
93C2×#11758200C2×C414yescomplemented
94C2×#11758201—22no—
95C2×#11758201—22no—
96C2×#11758201C2×C414yescomplemented
97SD16×D61—232no—
98C2×#11758189—22no—
99C2×#11758189—22no—
100C2×#11758189—22no—
101C22×#92418C2311yescharacteristic
102C22×#92418C2311yescharacteristic
103C2×C8×D61—22no—
104C2×C8×D61—22no—
105C2×C8×D61C2×C414yescomplemented
106C4×D244—22no—
107C4×D244—22no—
108D4×Dic61—22no—
109D4×Dic61—22no—
110#14519739—22no—
111#14519739—22no—
112C4×C22⋊D61—28no—
113#14519737—28no—
114#14519735—22no—
115#14519735—22no—
116#14519735—22no—
117#14519735D414yes—
118#14519734—22no—
119#14519734—22no—
120C2×C4⋊Dic61C2311yescharacteristic
121C2×C4⋊Dic61C2311yescharacteristic
122C2×#11758196D411yescharacteristic
123C2×#11758196D411yescharacteristic
124C2×C22⋊Dic61—21no—
125C2×#11758198—28no—
126C2×#11758198—21no—
127C2×#11758198—21no—
128C2×#11758198—21no—
129C2×#11758198—21no—
130C2×#11758198D411yescharacteristic
131C2×#11758198D411yescharacteristic
132C22⋊C4×D61—28no—
133C2×C4×Dic61—21no—
134C2×C4×Dic61—21no—
135C2×C4×Dic61C2311yescharacteristic
136#14519702—22no—
137#14519701—22no—
138#14519700—22no—
139#14519699—22no—
140#14519698—22no—
141#14519697—22no—
142#14519684—21no—
143#14519684—21no—
144#14519684—21no—
145#14519684—21no—
146#14519684—21no—
147#14519684—21no—
148C22×Q8×C61C2311yescharacteristic
149C22×D4×C61C2311yescharacteristic
150C23×C4×C61—21no—
151C2×SD16×C61—22no—
152C2×SD16×C61—22no—
153C2×SD16×C61C2×C414yescomplemented
154C22×C8×C61C2311yescharacteristic
155C22×C8×C61C2311yescharacteristic
156C4×D4×C61—22no—
157C4×D4×C61—22no—
158C2×C4⋊C4×C61C2311yescharacteristic
159C2×C4⋊C4×C61C2311yescharacteristic
160C2×C22⋊C4×C61—21no—
161C2×C42×C61C2311yescharacteristic
162#103×C61—22no—
163#102×C61—22no—
164#95×C61—21no—
165#95×C61—21no—
166C24×C61—21no—
167C23×D61—21no—
168C23×D61—24no—
169C23×D61—24no—
170C23×D61—24no—
171C23×D61—81no—
172C23×D61—81no—
173C23×D61—81no—
174C23×D61—81no—
175C23×D61C2×D411yescharacteristic
176C2×Q8×C61—21no—
177C2×Q8×C61—21no—
178C2×Q8×C61—21no—
179C2×Q8×C61—21no—
180C2×Q8×C61—21no—
181C2×Q8×C61C22×C412yes—
182C2×D4×C61—21no—
183C2×D4×C61—21no—
184C2×D4×C61—21no—
185C2×D4×C61C22×C412yes—
186C2×D4×C61C2×D412yes—
187C2×D4×C61C2×D412yes—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—24no—
191C22×C4×C61—21no—
192C22×C4×C61—81no—
193C22×C4×C61—81no—
194C22×C4×C61C2×D411yescharacteristic
195C22×C4×C61C2×D411yescharacteristic
196C22×C4×C61C2411yescharacteristic
197C2×C22⋊D61—24no—
198C2×C22⋊D61—24no—
199C2×C22⋊D61—24no—
200C22×Dic61—21no—
201C22×Dic61—21no—
202C22×Dic61—24no—
203C22×Dic61—21no—
204C22×Dic61—81no—
205C22×Dic61—81no—
206C22×Dic61C2×D411yescharacteristic
207C22×Dic61C2×D411yescharacteristic
208C22×Dic61C2×D411yescharacteristic
209Q8×D61—28no—
210Q8×D61—28no—
211Q8×D61—44no—
212Q8×D61—44no—
213D4×D61—28no—
214D4×D61—28no—
215D4×D61—28no—
216D4×D61C22⋊C4116yes—
217C2×D244—21no—
218C2×D244—21no—
219C2×D244—21no—
220C2×D244C22×C412yes—
221C2×D244C2×D412yes—
222C2×D244C2×D412yes—
223C2×C4×D61—24no—
224C2×C4×D61—24no—
225C2×C4×D61—24no—
226C2×C4×D61—42no—
227C2×C4×D61—42no—
228C2×C4×D61—81no—
229C2×C4×D61—81no—
230C2×C4×D61—81no—
231C2×C4×D61—81no—
232C2×C4×D61C22×C412yes—
233C2×C4×D61C2×D412yes—
234C2×C4×D61C2×D412yes—
235C2×C4×D61C2×D412yes—
236C2×C4×D61#4112yes—
237C2×C4×D61#4112yes—
238C2×Dic122—21no—
239C2×Dic122—21no—
240C2×Dic122—21no—
241C2×Dic122—21no—
242C2×Dic122—21no—
243C2×Dic122—24no—
244C2×Dic122—42no—
245C2×Dic122—42no—
246C2×Dic122C22×C412yes—
247SD16×C61—28no—
248C2×C8×C61—21no—
249C2×C8×C61—21no—
250C2×C8×C61—21no—
251C2×C8×C61—21no—
252C2×C8×C61—21no—
253C2×C8×C61C22×C412yes—
254C4⋊C4×C61—21no—
255C4⋊C4×C61—21no—
256C4⋊C4×C61—21no—
257C4⋊C4×C61C2×D412yes—
258C22⋊C4×C61—24no—
259C42×C61—21no—
260C42×C61—21no—
261C22⋊Dic61—24no—
262#11758201—28no—
263#11758200—28no—
264#11758198—24no—
265#11758198—24no—
266#11758198—22no—
267#11758198—24no—
268#11758198—22no—
269#11758198—42no—
270C4⋊Dic61—21no—
271C4⋊Dic61—21no—
272C4⋊Dic61—21no—
273C4⋊Dic61C2×D412yes—
274#11758196—22no—
275#11758196—22no—
276C4×Dic61—21no—
277C4×Dic61—21no—
278C4×Dic61—24no—
279C4×Dic61—42no—
280C2×#92418—21no—
281C2×#92418—21no—
282C2×#92418—21no—
283C2×#92418—21no—
284C2×#92418—21no—
285C2×#92418C22×C412yes—
286#11758190—28no—
287#11758189—44no—
288C8×D61—28no—
289C23×C61—22no—
290C23×C61—22no—
291C23×C61—22no—
292C23×C61—41no—
293C23×C61—41no—
294C23×C61—41no—
295C23×C61—41no—
296C23×C61C22×D411yescharacteristic
297C22×D61—21no—
298C22×D61—21no—
299C22×D61—21no—
300C22×D61—21no—
301C22×D61—22no—
302C22×D61—22no—
303C22×D61—22no—
304C22×D61—216no—
305C22×D61—41no—
306C22×D61—41no—
307C22×D61—41no—
308C22×D61—41no—
309C22×D61—84no—
310C22×D61—84no—
311C22×D61—84no—
312C22×D61—84no—
313C22×D61—84no—
314C22×D61—84no—
315C22×D61C4×D412yes—
316C22×D61#12012yes—
317C22×D61#12112yes—
318Q8×C61—22no—
319Q8×C61—22no—
320Q8×C61—41no—
321Q8×C61—41no—
322D4×C61—22no—
323D4×C61—22no—
324D4×C61—22no—
325D4×C61C2×C22⋊C414yes—
326C2×C4×C61—22no—
327C2×C4×C61—22no—
328C2×C4×C61—21no—
329C2×C4×C61—21no—
330C2×C4×C61—21no—
331C2×C4×C61—21no—
332C2×C4×C61—21no—
333C2×C4×C61—21no—
334C2×C4×C61—41no—
335C2×C4×C61—41no—
336C2×C4×C61—41no—
337C2×C4×C61—41no—
338C2×C4×C61—41no—
339C2×C4×C61—41no—
340C2×C4×C61—41no—
341C2×C4×C61—84no—
342C2×C4×C61C23×C411yescharacteristic
343C2×C4×C61C22×D411yescharacteristic
344C2×C4×C61C22×D411yescharacteristic
345C2×C4×C61C22×D411yescharacteristic
346C2×C4×C61C2×#4111yescharacteristic
347C2×C4×C61C2×#4111yescharacteristic
348C22⋊D61—216no—
349C2×Dic61—22no—
350C2×Dic61—21no—
351C2×Dic61—21no—
352C2×Dic61—22no—
353C2×Dic61—21no—
354C2×Dic61—21no—
355C2×Dic61—21no—
356C2×Dic61—21no—
357C2×Dic61—41no—
358C2×Dic61—41no—
359C2×Dic61—41no—
360C2×Dic61—41no—
361C2×Dic61—41no—
362C2×Dic61—41no—
363C2×Dic61—41no—
364C2×Dic61—84no—
365C2×Dic61C4×D412yes—
366C2×Dic61#12012yes—
367C2×Dic61#12112yes—
368D244—22no—
369D244—22no—
370D244—22no—
371D244C2×C22⋊C414yes—
372C4×D61—48no—
373C4×D61—84no—
374C4×D61—84no—
375C4×D61C2×C22⋊C414yes—
376C4×D61C4×D414yes—
377C4×D61#12114yes—
378C4×D61#12314yes—
379Dic122—22no—
380Dic122—22no—
381Dic122—41no—
382Dic122—41no—
383Dic122—48no—
384C8×C61—22no—
385C8×C61—41no—
386#92418—22no—
387#92418—41no—
388#20933—611nomaximal, Sylow
389C22×C61—24no—
390C22×C61—42no—
391C22×C61—42no—
392C22×C61—42no—
393C22×C61—42no—
394C22×C61—42no—
395C22×C61—42no—
396C22×C61C2×C4×D411yescharacteristic
397C22×C61C2×#12011yescharacteristic
398C22×C61C2×#12111yescharacteristic
399C22×C61#57711yescharacteristic
400C22×C61#57711yescharacteristic
401C22×C61#57711yescharacteristic
402C22×C61#57711yescharacteristic
403C2×D61—22no—
404C2×D61—22no—
405C2×D61—22no—
406C2×D61—22no—
407C2×D61—22no—
408C2×D61—22no—
409C2×D61—24no—
410C2×D61—42no—
411C2×D61—42no—
412C2×D61—42no—
413C2×D61—42no—
414C2×D61—42no—
415C2×D61—42no—
416C2×D61—816no—
417C2×D61#38614yes—
418C4×C61—41no—
419C4×C61—42no—
420C4×C61—41no—
421C4×C61—42no—
422C4×C61—81no—
423C4×C61C22×C22⋊C411yescharacteristic
424C4×C61C2×C4×D411yescharacteristic
425C4×C61C2×#12111yescharacteristic
426C4×C61C2×#12311yescharacteristic
427Dic61—41no—
428Dic61—42no—
429Dic61—41no—
430Dic61—42no—
431Dic61—81no—
432Dic61#38614yes—
433C23×SD16—611no—
434C2×#518—611no—
435C2×#419—611no—
436C2×#418—611no—
437#2310—611no—
438#1877—611no—
439#1877—611no—
440#1877—611no—
441#1877—611no—
442#1877—611no—
443#1877—611no—
444#1877—611no—
445#1877D6111yescharacteristic, complemented
446#1735—611no—
447#1729—611no—
448C2×C61—44no—
449C2×C61C2×#38611yescharacteristic
450C2×C61#294911yescharacteristic
451C2×C61#294911yescharacteristic
452C2×C61#300911yescharacteristic
453C2×C61#300911yescharacteristic
454C2×C61#304211yescharacteristic
455C2×C61#304211yescharacteristic
456D61—24no—
457D61—44no—
458C23×Q8—611no—
459C23×D4—611no—
460C22×SD16—611no—
461C22×SD16—611no—
462C22×SD16—618no—
463C22×SD16—611no—
464C22×SD16—1224no—
465C22×SD16—1224no—
466C22×SD16C2×D6111yescharacteristic
467C22×M16—611no—
468C23×C8—611no—
469#518—1224no—
470#518—1224no—
471C2×C4×D4—611no—
472C2×C4×D4—611no—
473C2×C4×D4—611no—
474C2×C4×D4—1221no—
475C2×C4×D4—1221no—
476C2×C4×D4C2×D6111yescharacteristic
477C2×#117—611no—
478C2×#117—611no—
479C2×#117—611no—
480C22×C22⋊C4—1221no—
481C22×C22⋊C4—1221no—
482#419—1224no—
483#418—1224no—
484C2×#103—611no—
485C2×#103—611no—
486C2×#103—611no—
487C2×#103C2×D6111yescharacteristic, complemented
488C2×#102—611no—
489C2×#102—611no—
490C2×#102—611no—
491C2×#102C2×D6111yescharacteristic
492#391—611no—
493#391—611no—
494#391—611no—
495#391—1221no—
496#391—1221no—
497#391C2×D6111yescharacteristic, complemented
498#381—1221no—
499#381—1221no—
500#340—611no—
501#340—611no—
502#340—611no—
503#340C2×D6111yescharacteristic, complemented
504#336—611no—
505#336—611no—
506#336—611no—
507#336C2×D6111yescharacteristic, complemented
508C61#2093311yescharacteristic, complemented, Sylow
509C25—1221no—
510C22×Q8—614no—
511C22×Q8—611no—
512C22×Q8—1221no—
513C22×Q8—1222no—
514C22×Q8—1222no—
515C22×Q8—1222no—
516C22×Q8—1222no—
517C22×Q8—1222no—
518C22×Q8C22×D6111yescharacteristic
519C22×D4—614no—
520C22×D4—614no—
521C22×D4—614no—
522C22×D4—611no—
523C22×D4—1222no—
524C22×D4—1222no—
525C22×D4—1222no—
526C22×D4—1221no—
527C22×D4C22×D6111yescharacteristic
528C23×C4—21no—
529C23×C4—611no—
530C23×C4—1221no—
531C23×C4—1221no—
532C23×C4—1221no—
533C23×C4—1221no—
534C2×SD16—22no—
535C2×SD16—22no—
536C2×SD16—614no—
537C2×SD16—614no—
538C2×SD16—614no—
539C2×SD16—1222no—
540C2×SD16—1222no—
541C2×SD16—12232no—
542C2×SD16—1222no—
543C2×SD16—1222no—
544C2×SD16—1222no—
545C2×SD16—1222no—
546C2×SD16C4×D6114yescomplemented
547C2×M16—1222no—
548C2×M16—1222no—
549C2×M16—1222no—
550C22×C8—611no—
551C22×C8—614no—
552C22×C8—611no—
553C22×C8—1222no—
554C22×C8—1222no—
555C22×C8C22×D6111yescharacteristic
556C22×C8C22×D6111yescharacteristic
557C4×D4—22no—
558C4×D4—22no—
559C4×D4—1222no—
560C4×D4—1222no—
561C4×D4—1228no—
562C4×D4—1222no—
563C4×D4—1222no—
564C4×D4—1228no—
565C4×D4—1222no—
566C4×D4—1222no—
567#117—614no—
568#117—1222no—
569#117—1222no—
570#117—1222no—
571#117—1222no—
572#117—1222no—
573C2×C4⋊C4—611no—
574C2×C4⋊C4—611no—
575C2×C4⋊C4—611no—
576C2×C4⋊C4—611no—
577C2×C4⋊C4C22×D6111yescharacteristic
578C2×C4⋊C4C22×D6111yescharacteristic
579C2×C22⋊C4—21no—
580C2×C22⋊C4—611no—
581C2×C22⋊C4—611no—
582C2×C22⋊C4—1228no—
583C2×C22⋊C4—1221no—
584C2×C22⋊C4—1221no—
585C2×C22⋊C4—1228no—
586C2×C22⋊C4—1221no—
587C2×C22⋊C4—1221no—
588C2×C22⋊C4—1221no—
589C2×C42—611no—
590C2×C42—1221no—
591C2×C42—1221no—
592C2×C42C22×D6111yescharacteristic
593#103—22no—
594#103—1222no—
595#103—1222no—
596#103—1222no—
597#102—22no—
598#102—1222no—
599#102—1222no—
600#102—1222no—
601#95—21no—
602#95—21no—
603#95—1221no—
604#95—1221no—
605#95—1221no—
606#95—1221no—
607#95—1221no—
608#95—1221no—
609C24—21no—
610C24—611no—
611C24—1224no—
612C24—1224no—
613C24—1224no—
614C24—1221no—
615C24—4881no—
616C24—4881no—
617C24—4881no—
618C24—4881no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8—612no—
625C2×Q8—1224no—
626C2×Q8—1228no—
627C2×Q8—1228no—
628C2×Q8—1221no—
629C2×Q8—1221no—
630C2×Q8—1221no—
631C2×Q8—1221no—
632C2×Q8—1221no—
633C2×Q8—2442no—
634C2×Q8—2442no—
635C2×Q8—2444no—
636C2×Q8—2444no—
637C2×Q8C2×C4×D6112yes—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—6116no—
642C2×D4—612no—
643C2×D4—612no—
644C2×D4—612no—
645C2×D4—1228no—
646C2×D4—1228no—
647C2×D4—1228no—
648C2×D4—1224no—
649C2×D4—1224no—
650C2×D4—1224no—
651C2×D4—1221no—
652C2×D4—1221no—
653C2×D4—1221no—
654C2×D4C2×C4×D6112yes—
655C2×D4D4×D6112yes—
656C2×D4D4×D6112yes—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—24no—
660C22×C4—21no—
661C22×C4—81no—
662C22×C4—81no—
663C22×C4—611no—
664C22×C4—612no—
665C22×C4—612no—
666C22×C4—612no—
667C22×C4—612no—
668C22×C4—612no—
669C22×C4—612no—
670C22×C4—611no—
671C22×C4—611no—
672C22×C4—1224no—
673C22×C4—1224no—
674C22×C4—1224no—
675C22×C4—1224no—
676C22×C4—1221no—
677C22×C4—1221no—
678C22×C4—1221no—
679C22×C4—4881no—
680C22×C4—4881no—
681C22×C4—4881no—
682C22×C4—4881no—
683C22×C4—4881no—
684C22×C4—4881no—
685C22×C4—2442no—
686C22×C4—2442no—
687C22×C4D4×D6111yescharacteristic
688C22×C4D4×D6111yescharacteristic
689C22×C4C23×D6111yescharacteristic
690SD16—28no—
691SD16—1228no—
692SD16—1228no—
693SD16—1228no—
694M16—2444no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—612no—
701C2×C8—1228no—
702C2×C8—1221no—
703C2×C8—1221no—
704C2×C8—1221no—
705C2×C8—1221no—
706C2×C8—1221no—
707C2×C8C2×C4×D6112yes—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—21no—
711C4⋊C4—612no—
712C4⋊C4—1222no—
713C4⋊C4—1222no—
714C4⋊C4—1221no—
715C4⋊C4—1221no—
716C4⋊C4—1221no—
717C4⋊C4D4×D6112yes—
718C22⋊C4—24no—
719C22⋊C4—1222no—
720C22⋊C4—1222no—
721C22⋊C4—1224no—
722C22⋊C4—1224no—
723C22⋊C4—1224no—
724C22⋊C4—1224no—
725C22⋊C4—2442no—
726C42—21no—
727C42—21no—
728C42—1224no—
729C42—1221no—
730C42—1221no—
731C42—2442no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—612no—
740C23—612no—
741C23—612no—
742C23—12216no—
743C23—1221no—
744C23—1221no—
745C23—1221no—
746C23—1221no—
747C23—1222no—
748C23—1222no—
749C23—1222no—
750C23—4884no—
751C23—4884no—
752C23—4884no—
753C23—4884no—
754C23—4884no—
755C23—4884no—
756C23—2441no—
757C23—2441no—
758C23—2441no—
759C23—2441no—
760C23C2×D4×D6111yescharacteristic
761Q8—22no—
762Q8—22no—
763Q8—41no—
764Q8—41no—
765Q8—1222no—
766Q8—1222no—
767Q8—2448no—
768Q8—2441no—
769Q8—2441no—
770D4—22no—
771D4—22no—
772D4—22no—
773D4—614no—
774D4—12216no—
775D4—1222no—
776D4—1222no—
777D4—1222no—
778D4C22⋊C4×D6114yes—
779C2×C4—22no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—22no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—84no—
795C2×C4—612no—
796C2×C4—612no—
797C2×C4—612no—
798C2×C4—614no—
799C2×C4—614no—
800C2×C4—614no—
801C2×C4—614no—
802C2×C4—1222no—
803C2×C4—1222no—
804C2×C4—1221no—
805C2×C4—1221no—
806C2×C4—1221no—
807C2×C4—1221no—
808C2×C4—1221no—
809C2×C4—1221no—
810C2×C4—4884no—
811C2×C4—4884no—
812C2×C4—4884no—
813C2×C4—2448no—
814C2×C4—2441no—
815C2×C4—2441no—
816C2×C4—2441no—
817C2×C4—2441no—
818C2×C4—2441no—
819C2×C4—2441no—
820C2×C4—2441no—
821C2×C4C22×C4×D6111yescharacteristic
822C2×C4C2×D4×D6111yescharacteristic
823C2×C4C2×D4×D6111yescharacteristic
824C2×C4C2×D4×D6111yescharacteristic
825C2×C4#41×D6111yescharacteristic
826C2×C4#41×D6111yescharacteristic
827C8—22no—
828C8—41no—
829C8—1222no—
830C8—2441no—
831C22—24no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—614no—
839C22—1222no—
840C22—1222no—
841C22—1222no—
842C22—1222no—
843C22—1222no—
844C22—1222no—
845C22—1224no—
846C22—48816no—
847C22—2442no—
848C22—2442no—
849C22—2442no—
850C22—2442no—
851C22—2442no—
852C22—2442no—
853C22C4×D4×D6111yescharacteristic
854C22#120×D6111yescharacteristic
855C22#121×D6111yescharacteristic
856C22#1684056811yescharacteristic
857C22#1684056911yescharacteristic
858C22#1684057111yescharacteristic
859C22#1684057211yescharacteristic
860C4—42no—
861C4—41no—
862C4—42no—
863C4—41no—
864C4—81no—
865C4—614no—
866C4—4881no—
867C4—2442no—
868C4—2441no—
869C4—2441no—
870C4—2442no—
871C4C2×C22⋊C4×D6111yescharacteristic
872C4C4×D4×D6111yescharacteristic
873C4#121×D6111yescharacteristic
874C4#123×D6111yescharacteristic
875C2—44no—
876C2—1224no—
877C2—2444no—
878C2#386×D6111yescharacteristic
879C2#2145467311yescharacteristic
880C2#2145467511yescharacteristic
881C2#2145509111yescharacteristic
882C2#2145509311yescharacteristic
883C2#2145532611yescharacteristic
884C2#2145532911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1877C2
socleC23×C61C22×D4
prime radicalC22×D4×D61C22
cosocleC22×C4×C61C24
hypercenter#1877D61
hypocenterC61#20933
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1877

Complements

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

NH ≅ G/Ntype
3. C2×#16839769C2semidirect
5. #21448402C2semidirect
6. #21446156C2semidirect
7. #21446155C2semidirect
8. #21446154C2semidirect
9. #21446153C2semidirect
10. #21446152C2semidirect
11. #21446151C2semidirect
12. #21446150C2semidirect
13. #21445534C2semidirect
14. #21445514C2semidirect
15. C61×#1877C2semidirect
23. C2×SD16×D61C4semidirect
40. C2×#14519702C22semidirect
41. C2×#14519701C22semidirect
42. C2×#14519700C22semidirect
46. #16839669C22semidirect
47. #16839668C22semidirect
48. #16839667C22semidirect
53. #16839525C22semidirect
54. #16839524C22semidirect
55. #16839524C22semidirect
56. #16839517C22semidirect
57. #16839516C22semidirect
58. #16839516C22semidirect
61. C2×#103×C61C22semidirect
63. C61×#391C22semidirect
64. C61×#340C22semidirect
65. C61×#336C22semidirect
74. C2×Q8×D61C2×C4semidirect
90. C2×#11758190C2×C4semidirect
93. C2×#11758200C2×C4semidirect
96. C2×#11758201C2×C4semidirect
105. C2×C8×D61C2×C4semidirect
153. C2×SD16×C61C2×C4semidirect
445. #1877D61semidirect
487. C2×#103C2×D61semidirect
497. #391C2×D61semidirect
503. #340C2×D61semidirect
507. #336C2×D61semidirect
508. C61#20933semidirect
546. C2×SD16C4×D61semidirect

Maximal subgroups

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

subgroupindex
C22×SD16×D612
C2×#168402342
C2×#168397692
C2×#168397652
#214484022
#214461562
#214461552
#214461542
#214461532
#214461522
#214461512
#214461502
#214455342
#214455142
C61×#18772
#2093361