Finite Group Databasebeta

← #29681380

Subgroups — #29681380

Order 15616.

1802 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519806C211yesmaximal, characteristic
2C2×C4×Q8×D61C211yesmaximal, characteristic, complemented
3C2×#16839760C211yesmaximal, characteristic
4C2×#16839769C211yesmaximal, characteristic, complemented
5#21448306C211yesmaximal, characteristic
6#21446177C211yesmaximal, characteristic, complemented
7#21446176C211yesmaximal, characteristic, complemented
8#21446171C211yesmaximal, characteristic, complemented
9#21446161C211yesmaximal, characteristic, complemented
10#21446160C211yesmaximal, characteristic, complemented
11#21446159C211yesmaximal, characteristic, complemented
12#21446158C211yesmaximal, characteristic, complemented
13#21445537C211yesmaximal, characteristic, complemented
14#21445511C211yesmaximal, characteristic, complemented
15C61×#1880C211yesmaximal, characteristic, complemented
16C22×#11758224C2211yescharacteristic
17C22×Q8×D61C2211yescharacteristic
18C2×#14519806—24no—
19C2×#14519806—24no—
20C2×#14519806C418yescomplemented
21C22×Dic244C2211yescharacteristic
22C22×#11758202C2211yescharacteristic
23C22×#11758200C2211yescharacteristic
24C22×#11758189C2211yescharacteristic
25C22×#11758189C2211yescharacteristic
26C2×Q8×Dic61C2211yescharacteristic
27C2×C4×Dic122—21no—
28C2×C4×Dic122C2211yescharacteristic
29C2×#14519742—21no—
30C2×#14519742C2211yescharacteristic
31C4×Q8×D61—24no—
32C4×Q8×D61—24no—
33C2×#14519735C2211yescharacteristic
34C2×C4⋊C4×D61—21no—
35C2×C4⋊C4×D61C2211yescharacteristic
36C2×C42×D61—21no—
37C2×C42×D61C2211yescharacteristic
38#16839769—24no—
39#16839760—24no—
40C2×#14519702C2211yescharacteristic
41C2×#14519702C2211yescharacteristic
42C2×#14519701C2211yescharacteristic
43C2×#14519700C2211yescharacteristic
44C2×#14519700C2211yescharacteristic
45C2×#14519698C2211yescharacteristic
46#16839668C2211yescharacteristic
47#16839667C2211yescharacteristic
48#16839665C2211yescharacteristic
49#16839638—21no—
50#16839638—21no—
51C22⋊C4×Dic61—21no—
52C22⋊C4×Dic61—21no—
53#16839525C2211yescharacteristic
54#16839524C2211yescharacteristic
55#16839524C2211yescharacteristic
56#16839517C2211yescharacteristic
57#16839516C2211yescharacteristic
58#16839516C2211yescharacteristic
59C22×SD16×C61C2211yescharacteristic
60C2×C4×Q8×C61C2211yescharacteristic
61C2×#103×C61C2211yescharacteristic
62C2×#102×C61C2211yescharacteristic
63C61×#390C2211yescharacteristic
64C61×#340C2211yescharacteristic
65C61×#336C2211yescharacteristic
66C2×#11758224—22no—
67C2×#11758224—22no—
68C2×#11758224—22no—
69C2×#11758224—22no—
70C2×#11758224—22no—
71C2×#11758224C2×C414yes—
72C22×Dic122—21no—
73C22×Dic122C2311yescharacteristic
74C22×Dic122C2311yescharacteristic
75C2×Q8×D61—22no—
76C2×Q8×D61—22no—
77C2×Q8×D61—22no—
78C2×Q8×D61C2×C414yes—
79C2×Q8×D61D414yes—
80C2×Q8×D61D414yes—
81C22×C22⋊D61—21no—
82C23×Dic61—21no—
83C22×C4×D61—21no—
84C22×C4×D61—21no—
85C22×C4×D61D411yescharacteristic
86C22×C4×D61D411yescharacteristic
87C22×C4×D61C2311yescharacteristic
88#14519806—232no—
89C2×Dic244—22no—
90C2×Dic244—22no—
91C2×Dic244C2×C414yescomplemented
92C2×#11758202—22no—
93C2×#11758202—22no—
94C2×#11758202C2×C414yescomplemented
95C2×#11758200—22no—
96C2×#11758200—22no—
97C2×#11758200C2×C414yescomplemented
98C2×#11758189—22no—
99C2×#11758189—22no—
100C2×#11758189—22no—
101C2×#11758189—22no—
102C2×#11758189—22no—
103C2×#11758189C2×C414yes—
104C22×#92418C2311yescharacteristic
105C22×#92418C2311yescharacteristic
106Q8×Dic61—22no—
107Q8×Dic61—22no—
108C4×Dic122—28no—
109C4×Dic122—22no—
110C4×Dic122—22no—
111#14519742—28no—
112#14519742—22no—
113#14519742—22no—
114#14519735—22no—
115#14519735—22no—
116C2×C4⋊Dic61—21no—
117C2×C4⋊Dic61C2311yescharacteristic
118C2×C4⋊Dic61C2311yescharacteristic
119C2×#11758196—21no—
120C2×#11758196—21no—
121C2×#11758196—21no—
122C4⋊C4×D61—28no—
123C4⋊C4×D61—22no—
124C4⋊C4×D61D414yes—
125C2×C22⋊Dic61—21no—
126C2×C22⋊Dic61—21no—
127C2×#11758198—21no—
128C2×C4×Dic61—21no—
129C2×C4×Dic61—21no—
130C2×C4×Dic61—21no—
131C2×C4×Dic61—21no—
132C2×C4×Dic61D411yescharacteristic
133C2×C4×Dic61D411yescharacteristic
134C2×C4×Dic61C2311yescharacteristic
135C42×D61—28no—
136C42×D61—22no—
137C42×D61—22no—
138#14519702—22no—
139#14519702—22no—
140#14519701—22no—
141#14519700—22no—
142#14519700—22no—
143#14519698—22no—
144#14519684—21no—
145#14519684—21no—
146#14519684—21no—
147#14519684—21no—
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×D61C2×D411yescharacteristic
168C2×Q8×C61—21no—
169C2×Q8×C61—21no—
170C2×Q8×C61—21no—
171C2×Q8×C61C22×C412yes—
172C2×Q8×C61C2×D412yes—
173C2×Q8×C61C2×D412yes—
174C2×D4×C61—21no—
175C2×D4×C61—21no—
176C2×D4×C61—21no—
177C2×D4×C61—21no—
178C2×D4×C61—21no—
179C2×D4×C61C22×C412yes—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61C2×D411yescharacteristic
184C22×C4×C61C2×D411yescharacteristic
185C22×C4×C61C2411yescharacteristic
186C2×C22⋊D61—24no—
187C2×C22⋊D61—42no—
188C2×C22⋊D61—42no—
189C22×Dic61—21no—
190C22×Dic61—21no—
191C22×Dic61—21no—
192C22×Dic61—24no—
193C22×Dic61—21no—
194C22×Dic61—42no—
195C22×Dic61—42no—
196C22×Dic61C2×D411yescharacteristic
197C22×Dic61C2×D411yescharacteristic
198C22×Dic61C2×D411yescharacteristic
199Q8×D61—28no—
200Q8×D61—28no—
201Q8×D61—28no—
202Q8×D61C22⋊C4116yescomplemented
203#11758224—28no—
204#11758224—28no—
205#11758224—44no—
206#11758224—44no—
207C2×C4×D61—24no—
208C2×C4×D61—24no—
209C2×C4×D61—22no—
210C2×C4×D61—24no—
211C2×C4×D61—22no—
212C2×C4×D61—22no—
213C2×C4×D61—24no—
214C2×C4×D61—22no—
215C2×C4×D61—41no—
216C2×C4×D61—41no—
217C2×C4×D61—42no—
218C2×C4×D61—42no—
219C2×C4×D61C22×C412yes—
220C2×C4×D61C2×D412yes—
221C2×C4×D61C2×D412yes—
222C2×C4×D61C2×D412yes—
223C2×C4×D61#4112yes—
224C2×C4×D61#4112yes—
225C2×Dic122—21no—
226C2×Dic122—21no—
227C2×Dic122—21no—
228C2×Dic122—24no—
229C2×Dic122—24no—
230C2×Dic122—24no—
231C2×Dic122—21no—
232C2×Dic122—21no—
233C2×Dic122—21no—
234C2×Dic122—21no—
235C2×Dic122—21no—
236C2×Dic122C22×C412yes—
237C2×Dic122C22×C412yes—
238C2×Dic122C2×D412yes—
239C2×Dic122C2×D412yes—
240SD16×C61—28no—
241C2×C8×C61—21no—
242C2×C8×C61—21no—
243C2×C8×C61—21no—
244C2×C8×C61—21no—
245C2×C8×C61—21no—
246C2×C8×C61C22×C412yes—
247C4⋊C4×C61—24no—
248C4⋊C4×C61—21no—
249C4⋊C4×C61—21no—
250C4⋊C4×C61—21no—
251C4⋊C4×C61C2×D412yes—
252C22⋊C4×C61—42no—
253C22⋊C4×C61—42no—
254C42×C61—24no—
255C42×C61—21no—
256C42×C61—21no—
257C22⋊Dic61—42no—
258C22⋊Dic61—42no—
259#11758202—28no—
260#11758200—28no—
261#11758198—42no—
262C4⋊Dic61—24no—
263C4⋊Dic61—21no—
264C4⋊Dic61—21no—
265C4⋊Dic61—21no—
266C4⋊Dic61C2×D412yes—
267#11758196—24no—
268#11758196—24no—
269#11758196—24no—
270C4×Dic61—24no—
271C4×Dic61—24no—
272C4×Dic61—24no—
273C4×Dic61—21no—
274C4×Dic61—21no—
275C4×Dic61—22no—
276C4×Dic61—22no—
277C4×Dic61—42no—
278C2×#92418—21no—
279C2×#92418—21no—
280C2×#92418—21no—
281C2×#92418—21no—
282C2×#92418—21no—
283C2×#92418C22×C412yes—
284Dic244—28no—
285#11758189—28no—
286#11758189—44no—
287C23×C61—22no—
288C23×C61—41no—
289C23×C61—41no—
290C23×C61—41no—
291C23×C61—41no—
292C23×C61—41no—
293C23×C61—41no—
294C23×C61C22×D411yescharacteristic
295C22×D61—21no—
296C22×D61—21no—
297C22×D61—21no—
298C22×D61—21no—
299C22×D61C4×D412yes—
300C22×D61#12012yes—
301C22×D61#12112yes—
302Q8×C61—22no—
303Q8×C61—22no—
304Q8×C61—22no—
305Q8×C61C2×C22⋊C414yes—
306D4×C61—22no—
307D4×C61—22no—
308D4×C61—41no—
309D4×C61—41no—
310C2×C4×C61—22no—
311C2×C4×C61—21no—
312C2×C4×C61—22no—
313C2×C4×C61—22no—
314C2×C4×C61—21no—
315C2×C4×C61—21no—
316C2×C4×C61—22no—
317C2×C4×C61—21no—
318C2×C4×C61—21no—
319C2×C4×C61—41no—
320C2×C4×C61—41no—
321C2×C4×C61—41no—
322C2×C4×C61—41no—
323C2×C4×C61—41no—
324C2×C4×C61#13712yescomplemented
325C2×C4×C61C23×C411yescharacteristic
326C2×C4×C61C22×D411yescharacteristic
327C2×C4×C61C22×D411yescharacteristic
328C2×C4×C61C22×D411yescharacteristic
329C2×C4×C61C2×#4111yescharacteristic
330C2×C4×C61C2×#4111yescharacteristic
331C22⋊D61—48no—
332C2×Dic61—22no—
333C2×Dic61—21no—
334C2×Dic61—22no—
335C2×Dic61—22no—
336C2×Dic61—21no—
337C2×Dic61—22no—
338C2×Dic61—21no—
339C2×Dic61—22no—
340C2×Dic61—21no—
341C2×Dic61—21no—
342C2×Dic61—41no—
343C2×Dic61—41no—
344C2×Dic61—41no—
345C2×Dic61—41no—
346C2×Dic61—48no—
347C2×Dic61—41no—
348C2×Dic61—41no—
349C2×Dic61—41no—
350C2×Dic61C4×D412yes—
351C2×Dic61#12012yes—
352C2×Dic61#12112yes—
353C2×Dic61#13712yescomplemented
354C4×D61—28no—
355C4×D61—216no—
356C4×D61—44no—
357C4×D61—48no—
358C4×D61C2×C22⋊C414yes—
359C4×D61C4×D414yes—
360C4×D61#12114yes—
361C4×D61#12314yes—
362Dic122—22no—
363Dic122—22no—
364Dic122—22no—
365Dic122—216no—
366Dic122—22no—
367Dic122—22no—
368Dic122—41no—
369Dic122—41no—
370Dic122C2×C22⋊C414yes—
371C8×C61—22no—
372C8×C61—41no—
373#92418—22no—
374#92418—41no—
375#20926—611nomaximal, Sylow
376C22×C61—42no—
377C22×C61—42no—
378C22×C61—42no—
379C22×C61—81no—
380C22×C61—81no—
381C22×C61—81no—
382C22×C61—81no—
383C22×C61C2×C4×D411yescharacteristic
384C22×C61C2×#12011yescharacteristic
385C22×C61C2×#12111yescharacteristic
386C22×C61C2×#13711yescharacteristic
387C22×C61C2×#13711yescharacteristic
388C22×C61#57511yescharacteristic
389C22×C61#57511yescharacteristic
390C2×D61—22no—
391C2×D61—22no—
392C2×D61—22no—
393C2×D61—22no—
394C2×D61—22no—
395C2×D61—22no—
396C2×D61#38614yes—
397C4×C61—22no—
398C4×C61—24no—
399C4×C61—41no—
400C4×C61—42no—
401C4×C61—81no—
402C4×C61C22×C22⋊C411yescharacteristic
403C4×C61C2×C4×D411yescharacteristic
404C4×C61C2×#12111yescharacteristic
405C4×C61C2×#12311yescharacteristic
406Dic61—22no—
407Dic61—24no—
408Dic61—41no—
409Dic61—42no—
410Dic61—42no—
411Dic61—81no—
412Dic61#38614yes—
413C22×#137—611no—
414C22×C4×Q8—611no—
415C2×#417—611no—
416C2×#419—611no—
417#2297—611no—
418#1880—611no—
419#1880—611no—
420#1880—611no—
421#1880D6111yescharacteristic, complemented
422#1878—611no—
423#1878—611no—
424#1878—611no—
425#1878—611no—
426#1736—611no—
427#1728—611no—
428C2×C61—82no—
429C2×C61C2×#38611yescharacteristic
430C2×C61C4×#13711yescharacteristic
431C2×C61C4×#13711yescharacteristic
432C2×C61#300411yescharacteristic
433C2×C61#300511yescharacteristic
434C2×C61#303711yescharacteristic
435C2×C61#303711yescharacteristic
436D61—24no—
437C22×#41—611no—
438C23×Q8—611no—
439C2×#137—618no—
440C2×#137—1224no—
441C2×#137—1224no—
442C22×Q16—611no—
443C22×Q16—611no—
444C22×SD16—611no—
445C22×SD16C2×D6111yescharacteristic
446C22×M16—611no—
447C22×M16—611no—
448C2×C4×Q8—611no—
449C2×C4×Q8—611no—
450C2×C4×Q8—611no—
451C2×C4×Q8—1221no—
452C2×C4×Q8—1221no—
453C2×C4×Q8—1224no—
454C2×C4×Q8—1224no—
455C2×C4×Q8C2×D6111yescharacteristic
456C2×#117—611no—
457C22×C4⋊C4—611no—
458C22×C4⋊C4—1221no—
459C22×C42—611no—
460C22×C42—1221no—
461#419—1224no—
462#417—1224no—
463C2×#103—611no—
464C2×#103—611no—
465C2×#103—611no—
466C2×#103—611no—
467C2×#103—611no—
468C2×#103C2×D6111yescharacteristic
469C2×#102—611no—
470C2×#102C2×D6111yescharacteristic
471#391—611no—
472#391—611no—
473#390—611no—
474#390C2×D6111yescharacteristic
475#386—1221no—
476#386—1221no—
477C4×C22⋊C4—1221no—
478C4×C22⋊C4—1221no—
479#340—611no—
480#340—611no—
481#340—611no—
482#340C2×D6111yescharacteristic
483#336—611no—
484#336—611no—
485#336—611no—
486#336C2×D6111yescharacteristic
487C61#2092611yescharacteristic, complemented, Sylow
488C2×#41—614no—
489C2×#41—1222no—
490C2×#41—1222no—
491C2×#41—1222no—
492C2×#41—1222no—
493C2×#41—1222no—
494C22×Q8—614no—
495C22×Q8—614no—
496C22×Q8—614no—
497C22×Q8—611no—
498C22×Q8—611no—
499C22×Q8—1221no—
500C22×Q8—1222no—
501C22×Q8—1222no—
502C22×Q8—1222no—
503C22×Q8C22×D6111yescharacteristic
504C22×D4—1221no—
505C22×D4C22×D6111yescharacteristic
506C23×C4—611no—
507C23×C4—611no—
508C23×C4—611no—
509C23×C4—1221no—
510C23×C4—1221no—
511C23×C4—1221no—
512#137—12232no—
513C2×Q16—614no—
514C2×Q16—614no—
515C2×Q16—1222no—
516C2×Q16—1222no—
517C2×Q16—1222no—
518C2×Q16—1222no—
519C2×SD16—22no—
520C2×SD16—22no—
521C2×SD16—614no—
522C2×SD16—1222no—
523C2×SD16—1222no—
524C2×SD16C4×D6114yescomplemented
525C2×M16—614no—
526C2×M16—1222no—
527C2×M16—1222no—
528C2×M16—1222no—
529C2×M16—1222no—
530C2×M16—1222no—
531C22×C8—611no—
532C22×C8—611no—
533C22×C8C22×D6111yescharacteristic
534C22×C8C22×D6111yescharacteristic
535C4×Q8—22no—
536C4×Q8—22no—
537C4×Q8—1222no—
538C4×Q8—1222no—
539C4×Q8—1228no—
540C4×Q8—1222no—
541C4×Q8—1228no—
542C4×Q8—1222no—
543C4×Q8—1222no—
544C4×Q8—1222no—
545#117—1222no—
546#117—1222no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—611no—
549C2×C4⋊C4—614no—
550C2×C4⋊C4—611no—
551C2×C4⋊C4—1222no—
552C2×C4⋊C4—1228no—
553C2×C4⋊C4—1221no—
554C2×C4⋊C4—1221no—
555C2×C4⋊C4—1221no—
556C2×C4⋊C4—1221no—
557C2×C4⋊C4C22×D6111yescharacteristic
558C2×C4⋊C4C22×D6111yescharacteristic
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—1221no—
562C2×C22⋊C4—1221no—
563C2×C22⋊C4—1221no—
564C2×C42—21no—
565C2×C42—611no—
566C2×C42—611no—
567C2×C42—611no—
568C2×C42—1222no—
569C2×C42—1222no—
570C2×C42—1228no—
571C2×C42—1221no—
572C2×C42—1221no—
573C2×C42—1221no—
574C2×C42—1221no—
575C2×C42C22×D6111yescharacteristic
576#103—22no—
577#103—1222no—
578#103—1222no—
579#103—1222no—
580#103—1222no—
581#103—1222no—
582#102—22no—
583#102—1222no—
584#95—1221no—
585#95—1221no—
586#95—1221no—
587#95—1221no—
588C24—21no—
589C24—611no—
590#41—1228no—
591#41—1228no—
592#41—2444no—
593#41—2444no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—6116no—
598C2×Q8—612no—
599C2×Q8—612no—
600C2×Q8—612no—
601C2×Q8—612no—
602C2×Q8—1224no—
603C2×Q8—1224no—
604C2×Q8—1224no—
605C2×Q8—1228no—
606C2×Q8—1228no—
607C2×Q8—1228no—
608C2×Q8—1221no—
609C2×Q8—1221no—
610C2×Q8—1221no—
611C2×Q8—1221no—
612C2×Q8—1221no—
613C2×Q8—1221no—
614C2×Q8—1221no—
615C2×Q8—1221no—
616C2×Q8C2×C4×D6112yes—
617C2×Q8D4×D6112yes—
618C2×Q8D4×D6112yes—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—1224no—
625C2×D4—2442no—
626C2×D4—2442no—
627C2×D4C2×C4×D6112yes—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—611no—
632C22×C4—612no—
633C22×C4—612no—
634C22×C4—612no—
635C22×C4—612no—
636C22×C4—612no—
637C22×C4—612no—
638C22×C4—611no—
639C22×C4—611no—
640C22×C4—1222no—
641C22×C4—1222no—
642C22×C4—1224no—
643C22×C4—1224no—
644C22×C4—1224no—
645C22×C4—1224no—
646C22×C4—1222no—
647C22×C4—1224no—
648C22×C4—1221no—
649C22×C4—1222no—
650C22×C4—1221no—
651C22×C4—1221no—
652C22×C4—1221no—
653C22×C4—2441no—
654C22×C4—2441no—
655C22×C4—2442no—
656C22×C4—2442no—
657C22×C4—2442no—
658C22×C4—2442no—
659C22×C4D4×D6111yescharacteristic
660C22×C4D4×D6111yescharacteristic
661C22×C4C23×D6111yescharacteristic
662Q16—1228no—
663Q16—1228no—
664SD16—28no—
665SD16—1228no—
666M16—1228no—
667M16—2444no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—612no—
674C2×C8—1221no—
675C2×C8—1221no—
676C2×C8—1221no—
677C2×C8—1221no—
678C2×C8—1221no—
679C2×C8C2×C4×D6112yes—
680C4⋊C4—24no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—612no—
685C4⋊C4—1224no—
686C4⋊C4—1224no—
687C4⋊C4—1224no—
688C4⋊C4—1224no—
689C4⋊C4—1221no—
690C4⋊C4—1221no—
691C4⋊C4—1221no—
692C4⋊C4D4×D6112yes—
693C22⋊C4—42no—
694C22⋊C4—42no—
695C22⋊C4—2442no—
696C22⋊C4—2442no—
697C22⋊C4—2442no—
698C42—24no—
699C42—21no—
700C42—21no—
701C42—1222no—
702C42—1222no—
703C42—1224no—
704C42—1224no—
705C42—1224no—
706C42—1221no—
707C42—1221no—
708C42—2442no—
709C23—22no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—612no—
717C23—612no—
718C23—612no—
719C23—1221no—
720C23—1221no—
721C23—1221no—
722C23—1221no—
723C23C2×D4×D6111yescharacteristic
724Q8—22no—
725Q8—22no—
726Q8—22no—
727Q8—614no—
728Q8—12216no—
729Q8—1222no—
730Q8—1222no—
731Q8—1222no—
732Q8—1222no—
733Q8—1222no—
734Q8—2441no—
735Q8—2441no—
736Q8C22⋊C4×D6114yes—
737D4—22no—
738D4—22no—
739D4—41no—
740D4—41no—
741D4—2448no—
742C2×C4—22no—
743C2×C4—21no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—22no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—612no—
757C2×C4—612no—
758C2×C4—612no—
759C2×C4—614no—
760C2×C4—614no—
761C2×C4—614no—
762C2×C4—614no—
763C2×C4—612no—
764C2×C4—12216no—
765C2×C4—1228no—
766C2×C4—1222no—
767C2×C4—1221no—
768C2×C4—1222no—
769C2×C4—1222no—
770C2×C4—1221no—
771C2×C4—1222no—
772C2×C4—1222no—
773C2×C4—1221no—
774C2×C4—1221no—
775C2×C4—1221no—
776C2×C4—2444no—
777C2×C4—2448no—
778C2×C4—2448no—
779C2×C4—2441no—
780C2×C4—2441no—
781C2×C4—2441no—
782C2×C4—2441no—
783C2×C4—2441no—
784C2×C4—2441no—
785C2×C4—2441no—
786C2×C4#1451980612yescomplemented
787C2×C4C22×C4×D6111yescharacteristic
788C2×C4C2×D4×D6111yescharacteristic
789C2×C4C2×D4×D6111yescharacteristic
790C2×C4C2×D4×D6111yescharacteristic
791C2×C4#41×D6111yescharacteristic
792C2×C4#41×D6111yescharacteristic
793C8—22no—
794C8—41no—
795C8—1222no—
796C8—2441no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—614no—
805C22—1222no—
806C22—1222no—
807C22—1222no—
808C22—1222no—
809C22—1222no—
810C22—1222no—
811C22C4×D4×D6111yescharacteristic
812C22#120×D6111yescharacteristic
813C22#121×D6111yescharacteristic
814C22#137×D6111yescharacteristic
815C22C2×#1451980611yescharacteristic
816C22#1684055811yescharacteristic
817C22#1684055911yescharacteristic
818C4—24no—
819C4—22no—
820C4—41no—
821C4—42no—
822C4—81no—
823C4—614no—
824C4—1224no—
825C4—1222no—
826C4—4881no—
827C4—2442no—
828C4—2441no—
829C4—2442no—
830C4C2×C22⋊C4×D6111yescharacteristic
831C4C4×D4×D6111yescharacteristic
832C4#121×D6111yescharacteristic
833C4#123×D6111yescharacteristic
834C2—82no—
835C2—1224no—
836C2#386×D6111yescharacteristic
837C2C4×#1451980611yescharacteristic
838C2#2145464111yescharacteristic
839C2#2145505011yescharacteristic
840C2#2145505711yescharacteristic
841C2#2145528611yescharacteristic
842C2#2145528911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1880C2
socleC23×C61C22×D4
prime radicalC22×#11758224C22
cosocleC22×C4×C61C24
hypercenter#1880D61
hypocenterC61#20926
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×C4×Q8×D61C2semidirect
4. C2×#16839769C2semidirect
6. #21446177C2semidirect
7. #21446176C2semidirect
8. #21446171C2semidirect
9. #21446161C2semidirect
10. #21446160C2semidirect
11. #21446159C2semidirect
12. #21446158C2semidirect
13. #21445537C2semidirect
14. #21445511C2semidirect
15. C61×#1880C2semidirect
20. C2×#14519806C4semidirect
91. C2×Dic244C2×C4semidirect
94. C2×#11758202C2×C4semidirect
97. C2×#11758200C2×C4semidirect
152. C2×SD16×C61C2×C4semidirect
202. Q8×D61C22⋊C4semidirect
324. C2×C4×C61#137semidirect
353. C2×Dic61#137semidirect
421. #1880D61semidirect
487. C61#20926semidirect
524. C2×SD16C4×D61semidirect
786. C2×C4#14519806semidirect

Maximal subgroups

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

subgroupindex
C22×#145198062
C2×C4×Q8×D612
C2×#168397602
C2×#168397692
#214483062
#214461772
#214461762
#214461712
#214461612
#214461602
#214461592
#214461582
#214455372
#214455112
C61×#18802
#2092661