Finite Group Databasebeta

← #29611462

Subgroups — #29611462

Order 15616.

2558 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519753C211yesmaximal, characteristic, complemented
2C22×#14519737C211yesmaximal, characteristic
3C2×#16839681C211yesmaximal, characteristic, complemented
4C2×#16839634C212yesmaximal, complemented
5#21444073C211yesmaximal, characteristic, complemented
6#21444064C211yesmaximal, characteristic, complemented
7#21444063C212yesmaximal, complemented
8#21444058C212yesmaximal
9#21444050C212yesmaximal, complemented
10#21444040C211yesmaximal, characteristic, complemented
11C2×C61×#393C211yesmaximal, characteristic, complemented
12C23×C22⋊D61C2211yescharacteristic
13C24×Dic61C2211yescharacteristic
14C23×C4×D61C2211yescharacteristic
15C2×#14519753—28no—
16C2×#14519753—24no—
17C2×#14519737—24no—
18C2×#14519737—24no—
19C2×#14519737—24no—
20C22×C4⋊Dic61C2211yescharacteristic
21C22×#11758196C2212yes—
22C22×#11758196C2211yescharacteristic
23C22×#11758196C2212yes—
24C22×C22⋊Dic61C2212yes—
25C22×#11758198C2211yescharacteristic
26C22×#11758198C2212yes—
27C22×#11758198C2212yes—
28C22×C4×Dic61C2211yescharacteristic
29#16839681—24no—
30#16839634—28no—
31C2×#14519684C2212yes—
32C2×#14519684C2212yes—
33C2×#14519684C2211yescharacteristic
34C2×#14519684C2212yes—
35C2×#14519684C2212yes—
36C2×#14519684C2212yes—
37C23×Q8×C61C2211yescharacteristic
38C22×C22⋊C4×C61C2212yes—
39C22×C22⋊C4×C61C2211yescharacteristic
40C61×#393—24no—
41C2×#95×C61C2211yescharacteristic
42C2×#95×C61C2212yes—
43C24×D61C2311yescharacteristic
44C22×C22⋊D61—22no—
45C22×C22⋊D61—22no—
46C22×C22⋊D61—22no—
47C22×C22⋊D61—22no—
48C22×C22⋊D61—22no—
49C22×C22⋊D61—22no—
50C22×C22⋊D61Q814yescomplemented
51C23×Dic61—22no—
52C23×Dic61—22no—
53C23×Dic61—22no—
54C23×Dic61—24no—
55C23×Dic61—42no—
56C23×Dic61C2312yes—
57C23×Dic61C2311yescharacteristic
58C23×Dic61C2312yes—
59C23×Dic61C2311yescharacteristic
60C23×Dic61C2311yescharacteristic
61C22×C4×D61—22no—
62C22×C4×D61—22no—
63C22×C4×D61—24no—
64C22×C4×D61—42no—
65C22×C4×D61D414yes—
66#14519753—232no—
67#14519737—232no—
68C2×C4⋊Dic61—22no—
69C2×C4⋊Dic61—24no—
70C2×#11758196—22no—
71C2×#11758196—22no—
72C2×#11758196—24no—
73C2×#11758196—24no—
74C2×#11758196—24no—
75C2×#11758196—24no—
76C2×#11758196—42no—
77C2×#11758196D414yes—
78C2×#11758196D418yescomplemented
79C2×C22⋊Dic61—24no—
80C2×C22⋊Dic61—24no—
81C2×C22⋊Dic61—24no—
82C2×#11758198—22no—
83C2×#11758198—24no—
84C2×#11758198—22no—
85C2×#11758198—24no—
86C2×#11758198—22no—
87C2×#11758198—24no—
88C2×#11758198—24no—
89C2×#11758198—24no—
90C2×#11758198—42no—
91C2×C4×Dic61—22no—
92C2×C4×Dic61—22no—
93C2×C4×Dic61—22no—
94#14519684—22no—
95#14519684—24no—
96#14519684—24no—
97#14519684—24no—
98#14519684—24no—
99#14519684—24no—
100C25×C61C2311yescharacteristic
101C22×Q8×C61—24no—
102C22×Q8×C61—22no—
103C22×Q8×C61—22no—
104C22×Q8×C61—22no—
105C22×Q8×C61—42no—
106C23×C4×C61C2312yes—
107C23×C4×C61C2311yescharacteristic
108C23×C4×C61C2312yes—
109C23×C4×C61C2311yescharacteristic
110C2×C22⋊C4×C61—22no—
111C2×C22⋊C4×C61—22no—
112C2×C22⋊C4×C61—24no—
113C2×C22⋊C4×C61—24no—
114C2×C22⋊C4×C61—42no—
115C2×C22⋊C4×C61D414yes—
116#95×C61—24no—
117#95×C61—22no—
118C24×C61—21no—
119C24×C61—21no—
120C24×C61—22no—
121C24×C61—21no—
122C24×C61—21no—
123C24×C61—22no—
124C24×C61—22no—
125C24×C61—22no—
126C24×C61C2×D412yes—
127C24×C61C2×Q812yes—
128C24×C61#4112yes—
129C24×C61C2411yescharacteristic
130C23×D61—21no—
131C23×D61—21no—
132C23×D61—22no—
133C23×D61—21no—
134C23×D61—21no—
135C23×D61—22no—
136C23×D61—22no—
137C23×D61—22no—
138C23×D61C2×D412yes—
139C23×D61C2×Q812yes—
140C23×D61#4112yes—
141C2×Q8×C61—28no—
142C2×Q8×C61—48no—
143C2×Q8×C61—48no—
144C2×Q8×C61—44no—
145C2×Q8×C61—44no—
146C22×C4×C61—22no—
147C22×C4×C61—22no—
148C22×C4×C61—22no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—22no—
152C22×C4×C61—22no—
153C22×C4×C61—22no—
154C22×C4×C61—22no—
155C22×C4×C61—22no—
156C22×C4×C61—22no—
157C22×C4×C61—22no—
158C22×C4×C61—22no—
159C22×C4×C61—22no—
160C22×C4×C61—22no—
161C22×C4×C61—22no—
162C22×C4×C61—22no—
163C22×C4×C61—22no—
164C22×C4×C61—22no—
165C22×C4×C61C2×D414yes—
166C22×C4×C61C2×D412yes—
167C22×C4×C61C2×D412yes—
168C22×C4×C61C2×D412yes—
169C22×C4×C61C2×D412yes—
170C2×C22⋊D61—28no—
171C2×C22⋊D61—28no—
172C2×C22⋊D61—28no—
173C2×C22⋊D61—28no—
174C2×C22⋊D61—28no—
175C2×C22⋊D61—28no—
176C2×C22⋊D61—28no—
177C22×Dic61—21no—
178C22×Dic61—21no—
179C22×Dic61—21no—
180C22×Dic61—21no—
181C22×Dic61—21no—
182C22×Dic61—21no—
183C22×Dic61—22no—
184C22×Dic61—28no—
185C22×Dic61—22no—
186C22×Dic61—21no—
187C22×Dic61—21no—
188C22×Dic61—22no—
189C22×Dic61—22no—
190C22×Dic61—22no—
191C22×Dic61—22no—
192C22×Dic61—22no—
193C22×Dic61—22no—
194C22×Dic61—22no—
195C22×Dic61—22no—
196C22×Dic61—22no—
197C22×Dic61—22no—
198C22×Dic61—22no—
199C22×Dic61—22no—
200C22×Dic61—22no—
201C22×Dic61—48no—
202C22×Dic61—48no—
203C22×Dic61—44no—
204C22×Dic61—44no—
205C22×Dic61C2×D412yes—
206C22×Dic61C2×D414yes—
207C22×Dic61C2×D414yes—
208C22×Dic61C2×D412yes—
209C22×Dic61C2×D412yes—
210C22×Dic61C2×Q812yes—
211C22×Dic61#4114yes—
212C22×Dic61#4112yes—
213C2×C4×D61—28no—
214C2×C4×D61—28no—
215C2×C4×D61—44no—
216C2×C4×D61—48no—
217C2×C4×D61—48no—
218C22⋊C4×C61—28no—
219C22⋊C4×C61—48no—
220C22⋊Dic61—216no—
221#11758198—28no—
222#11758198—216no—
223#11758198—48no—
224C4⋊Dic61—28no—
225#11758196—28no—
226#11758196—216no—
227#11758196—48no—
228C4×Dic61—28no—
229C23×C61—22no—
230C23×C61—22no—
231C23×C61—22no—
232C23×C61—24no—
233C23×C61—22no—
234C23×C61—22no—
235C23×C61—22no—
236C23×C61—24no—
237C23×C61—24no—
238C23×C61—24no—
239C23×C61—24no—
240C23×C61—24no—
241C23×C61—41no—
242C23×C61—41no—
243C23×C61—42no—
244C23×C61—41no—
245C23×C61—41no—
246C23×C61—42no—
247C23×C61—42no—
248C23×C61—42no—
249C23×C61—42no—
250C23×C61—42no—
251C23×C61C22⋊Q814yescomplemented
252C23×C61C22×D411yescharacteristic
253C23×C61C22×D411yescharacteristic
254C23×C61C22×D411yescharacteristic
255C23×C61C22×D412yes—
256C23×C61C22×Q811yescharacteristic
257C23×C61C2×#4111yescharacteristic
258C23×C61C2×#4111yescharacteristic
259C23×C61C2×#4111yescharacteristic
260C23×C61C2×#4112yes—
261C23×C61H(5,𝔽2)12yes—
262C23×C612−1+412yes—
263C22×D61—22no—
264C22×D61—22no—
265C22×D61—22no—
266C22×D61—22no—
267C22×D61—22no—
268C22×D61—22no—
269C22×D61—22no—
270C22×D61—22no—
271C22×D61—22no—
272C22×D61—22no—
273C22×D61—24no—
274C22×D61—24no—
275C22×D61—24no—
276C22×D61—24no—
277C22×D61—42no—
278C22×D61—42no—
279C22×D61—42no—
280C22×D61—42no—
281C22×D61—42no—
282C22×D61—42no—
283C22×D61—42no—
284C22×D61—42no—
285C22×D61C22⋊Q814yes—
286Q8×C61—416no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—24no—
290C2×C4×C61—24no—
291C2×C4×C61—22no—
292C2×C4×C61—24no—
293C2×C4×C61—24no—
294C2×C4×C61—24no—
295C2×C4×C61—24no—
296C2×C4×C61—42no—
297C2×C4×C61—41no—
298C2×C4×C61—42no—
299C2×C4×C61—41no—
300C2×C4×C61—42no—
301C2×C4×C61—42no—
302C2×C4×C61—42no—
303C2×C4×C61—42no—
304C2×C4×C61—42no—
305C2×C4×C61—42no—
306C2×C4×C61—42no—
307C2×C4×C61—42no—
308C2×C4×C61—42no—
309C2×C4×C61—42no—
310C2×C4×C61#12014yes—
311C22⋊D61—232no—
312C2×Dic61—22no—
313C2×Dic61—22no—
314C2×Dic61—22no—
315C2×Dic61—22no—
316C2×Dic61—22no—
317C2×Dic61—22no—
318C2×Dic61—22no—
319C2×Dic61—22no—
320C2×Dic61—24no—
321C2×Dic61—24no—
322C2×Dic61—24no—
323C2×Dic61—22no—
324C2×Dic61—24no—
325C2×Dic61—24no—
326C2×Dic61—24no—
327C2×Dic61—24no—
328C2×Dic61—24no—
329C2×Dic61—24no—
330C2×Dic61—416no—
331C2×Dic61—41no—
332C2×Dic61—42no—
333C2×Dic61—42no—
334C2×Dic61—42no—
335C2×Dic61—42no—
336C2×Dic61—42no—
337C2×Dic61—41no—
338C2×Dic61—42no—
339C2×Dic61—42no—
340C2×Dic61—42no—
341C2×Dic61—42no—
342C2×Dic61#12014yes—
343C2×Dic61C22⋊Q814yescomplemented
344C4×D61—416no—
345#14723—611nomaximal, Sylow
346C22×C61—24no—
347C22×C61—28no—
348C22×C61—42no—
349C22×C61—42no—
350C22×C61—42no—
351C22×C61—42no—
352C22×C61—42no—
353C22×C61—42no—
354C22×C61—44no—
355C22×C61—44no—
356C22×C61—44no—
357C22×C61C2×#12011yescharacteristic
358C22×C61C2×#12011yescharacteristic
359C22×C61C2×C22⋊Q811yescharacteristic
360C22×C61C2×C22⋊Q811yescharacteristic
361C22×C61C2×C22⋊Q811yescharacteristic
362C22×C61#52511yescharacteristic
363C22×C61#52511yescharacteristic
364C22×C61#52511yescharacteristic
365C22×C61#52512yes—
366C22×C61#53211yescharacteristic
367C22×C61#53212yes—
368C22×C61#53411yescharacteristic
369C22×C61#53611yescharacteristic
370C22×C61#53912yes—
371C22×C61#54212yes—
372C22×C61D4212yes—
373C22×C61D4212yes—
374C22×C61#54712yes—
375C22×C61#54812yes—
376C22×C61#54812yes—
377C22×C61D4×Q812yes—
378C22×C61#55112yes—
379C22×C61#55412yes—
380C2×D61—24no—
381C2×D61—24no—
382C2×D61—24no—
383C2×D61—42no—
384C2×D61—42no—
385C2×D61—42no—
386C2×D61—42no—
387C2×D61—44no—
388C2×D61—44no—
389C2×D61—44no—
390C2×D61—44no—
391C4×C61—24no—
392C4×C61—44no—
393C4×C61—42no—
394C4×C61—82no—
395Dic61—24no—
396Dic61—24no—
397Dic61—44no—
398Dic61—42no—
399Dic61—44no—
400C22×C22⋊Q8—611no—
401C22×C4×D4—611no—
402C2×#395—611no—
403C2×#393D6111yescharacteristic, complemented
404C2×#385—612no—
405#1441—611no—
406#1439—612no—
407#1439—611no—
408#1438—612no—
409#1436—612no—
410C22⋊#95—611no—
411C2×C61—44no—
412C2×C61#238811yescharacteristic
413C2×C61#240311yescharacteristic
414C2×C61#240911yescharacteristic
415C2×C61#243211yescharacteristic
416C2×C61#244912yes—
417C2×C61#245212yes—
418C2×C61#246112yes—
419C2×C61#246312yes—
420C2×C61#256411yescharacteristic
421C2×C61#263811yescharacteristic
422C2×C61#284811yescharacteristic
423D61—44no—
424C23×Q8C2×D6111yescharacteristic
425C23×D4—611no—
426C24×C4—611no—
427C24×C4—611no—
428C2×C22⋊Q8—1228no—
429C2×C22⋊Q8—1224no—
430C2×C4×D4—1224no—
431C2×C4×D4—1224no—
432C2×C4×D4—1224no—
433C22×C4⋊C4—611no—
434C22×C4⋊C4—612no—
435C22×C4⋊C4—611no—
436C22×C4⋊C4—612no—
437C22×C22⋊C4—612no—
438C22×C22⋊C4—611no—
439C22×C22⋊C4—612no—
440C22×C22⋊C4—612no—
441C22×C22⋊C4C2×D6112yes—
442C22×C22⋊C4C2×D6111yescharacteristic
443C22×C42—611no—
444#395—1224no—
445#393—24no—
446#385—1228no—
447C2×#95—611no—
448C2×#95—612no—
449C2×#95—612no—
450C2×#95—612no—
451C2×#95—612no—
452C2×#95—612no—
453C2×#95C2×D6111yescharacteristic
454C2×#95C2×D6112yes—
455C61#1472311yescharacteristic, complemented, Sylow
456C25—611no—
457C25C22×D6111yescharacteristic
458C22×Q8—24no—
459C22×Q8—22no—
460C22×Q8—22no—
461C22×Q8—22no—
462C22×Q8—42no—
463C22×D4—614no—
464C22×D4—1222no—
465C22×D4—1222no—
466C22×D4—1222no—
467C22×D4—1222no—
468C22×D4—1222no—
469C22×D4—1222no—
470C23×C4—611no—
471C23×C4—611no—
472C23×C4—612no—
473C23×C4—612no—
474C23×C4—611no—
475C23×C4—614no—
476C23×C4—1224no—
477C23×C4—1222no—
478C23×C4—1222no—
479C23×C4—1224no—
480C23×C4—1222no—
481C23×C4—1222no—
482C23×C4—1222no—
483C23×C4—2442no—
484C23×C4—2442no—
485C23×C4C22×D6112yes—
486C23×C4C22×D6112yes—
487C23×C4C22×D6111yescharacteristic
488C23×C4C22×D6111yescharacteristic
489C22⋊Q8—12232no—
490C4×D4—12232no—
491C2×C4⋊C4—614no—
492C2×C4⋊C4—618no—
493C2×C4⋊C4—1224no—
494C2×C4⋊C4—1224no—
495C2×C4⋊C4—1224no—
496C2×C4⋊C4—1222no—
497C2×C4⋊C4—1222no—
498C2×C4⋊C4—1222no—
499C2×C4⋊C4—1224no—
500C2×C4⋊C4—1224no—
501C2×C4⋊C4—2442no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—42no—
507C2×C22⋊C4—1222no—
508C2×C22⋊C4—1224no—
509C2×C22⋊C4—1222no—
510C2×C22⋊C4—1224no—
511C2×C22⋊C4—1224no—
512C2×C22⋊C4—1224no—
513C2×C22⋊C4—1224no—
514C2×C22⋊C4—1224no—
515C2×C22⋊C4—1222no—
516C2×C22⋊C4—1224no—
517C2×C22⋊C4—1224no—
518C2×C22⋊C4—2442no—
519C2×C22⋊C4C22⋊D6114yes—
520C2×C42—1222no—
521C2×C42—1222no—
522C2×C42—1222no—
523#95—24no—
524#95—22no—
525#95—1224no—
526#95—1224no—
527#95—1224no—
528#95—1224no—
529#95—1224no—
530#95—1222no—
531C24—22no—
532C24—21no—
533C24—21no—
534C24—22no—
535C24—21no—
536C24—21no—
537C24—22no—
538C24—22no—
539C24—612no—
540C24—612no—
541C24—612no—
542C24—1222no—
543C24—1221no—
544C24—1221no—
545C24—1222no—
546C24—1221no—
547C24—1221no—
548C24—1222no—
549C24—1222no—
550C24Q8×D6112yes—
551C24#1175822612yes—
552C24C2×C22⋊D6112yes—
553C24C23×D6111yescharacteristic
554C2×Q8—28no—
555C2×Q8—48no—
556C2×Q8—48no—
557C2×Q8—44no—
558C2×Q8—44no—
559C2×D4—1228no—
560C2×D4—1228no—
561C2×D4—1228no—
562C2×D4—1228no—
563C2×D4—1228no—
564C2×D4—1228no—
565C2×D4—1228no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—612no—
586C22×C4—614no—
587C22×C4—612no—
588C22×C4—612no—
589C22×C4—612no—
590C22×C4—614no—
591C22×C4—612no—
592C22×C4—614no—
593C22×C4—1228no—
594C22×C4—1221no—
595C22×C4—1221no—
596C22×C4—1221no—
597C22×C4—1221no—
598C22×C4—1221no—
599C22×C4—1221no—
600C22×C4—1222no—
601C22×C4—1228no—
602C22×C4—1222no—
603C22×C4—1222no—
604C22×C4—1222no—
605C22×C4—1222no—
606C22×C4—1222no—
607C22×C4—1221no—
608C22×C4—1221no—
609C22×C4—1222no—
610C22×C4—1222no—
611C22×C4—1222no—
612C22×C4—1222no—
613C22×C4—1222no—
614C22×C4—1222no—
615C22×C4—1222no—
616C22×C4—1222no—
617C22×C4—1222no—
618C22×C4—1228no—
619C22×C4—2444no—
620C22×C4—2448no—
621C22×C4—2448no—
622C22×C4—2444no—
623C22×C4—2448no—
624C22×C4—2448no—
625C22×C4—2444no—
626C22×C4D4×D6114yes—
627C22×C4D4×D6112yes—
628C22×C4D4×D6112yes—
629C22×C4C2×C22⋊D6112yes—
630C22×C4C2×C22⋊D6112yes—
631C4⋊C4—12216no—
632C4⋊C4—1228no—
633C4⋊C4—1228no—
634C4⋊C4—2448no—
635C22⋊C4—28no—
636C22⋊C4—48no—
637C22⋊C4—1228no—
638C22⋊C4—12216no—
639C22⋊C4—12216no—
640C22⋊C4—2448no—
641C42—1228no—
642C23—24no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—24no—
648C23—22no—
649C23—22no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—41no—
655C23—42no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—614no—
665C23—1224no—
666C23—1222no—
667C23—1222no—
668C23—1222no—
669C23—1222no—
670C23—1222no—
671C23—1222no—
672C23—1222no—
673C23—1222no—
674C23—1222no—
675C23—1222no—
676C23—1224no—
677C23—1224no—
678C23—1224no—
679C23—2442no—
680C23—2442no—
681C23—2442no—
682C23—2442no—
683C23—2442no—
684C23—2442no—
685C23—2442no—
686C23—2442no—
687C23#1451975314yescomplemented
688C23C2×D4×D6111yescharacteristic
689C23C2×D4×D6112yes—
690C23C2×D4×D6111yescharacteristic
691C23C22×C22⋊D6111yescharacteristic
692C23C2×Q8×D6111yescharacteristic
693C23#41×D6112yes—
694C23#41×D6111yescharacteristic
695C23#41×D6111yescharacteristic
696C23C2×#1175822611yescharacteristic
697C23#1451982212yes—
698C23#1451982412yes—
699Q8—416no—
700D4—12232no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—42no—
711C2×C4—41no—
712C2×C4—42no—
713C2×C4—41no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—614no—
725C2×C4—614no—
726C2×C4—1222no—
727C2×C4—1222no—
728C2×C4—1222no—
729C2×C4—1222no—
730C2×C4—1222no—
731C2×C4—1222no—
732C2×C4—1222no—
733C2×C4—1222no—
734C2×C4—1224no—
735C2×C4—1224no—
736C2×C4—1224no—
737C2×C4—1222no—
738C2×C4—1224no—
739C2×C4—1224no—
740C2×C4—1224no—
741C2×C4—1224no—
742C2×C4—1224no—
743C2×C4—1224no—
744C2×C4—24416no—
745C2×C4—24416no—
746C2×C4—2441no—
747C2×C4—2442no—
748C2×C4—2442no—
749C2×C4—2442no—
750C2×C4—2442no—
751C2×C4—2442no—
752C2×C4—2441no—
753C2×C4—2442no—
754C2×C4—2442no—
755C2×C4—2442no—
756C2×C4—2442no—
757C2×C4#1451974514yes—
758C22—24no—
759C22—28no—
760C22—44no—
761C22—42no—
762C22—44no—
763C22—42no—
764C22—44no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—1224no—
770C22—1224no—
771C22—1224no—
772C22—2444no—
773C22—2442no—
774C22—2444no—
775C22—2444no—
776C22—2442no—
777C22—2444no—
778C22—2442no—
779C22—2442no—
780C22#120×D6111yescharacteristic
781C22C2×#1451974511yescharacteristic
782C22C22⋊Q8×D6111yescharacteristic
783C22C22⋊Q8×D6111yescharacteristic
784C22C2×#1451975311yescharacteristic
785C22#1684026911yescharacteristic
786C22#1684027511yescharacteristic
787C22#1684027511yescharacteristic
788C22#1684027512yes—
789C22#1684031112yes—
790C22#1684031111yescharacteristic
791C22#1684032211yescharacteristic
792C22#1684033211yescharacteristic
793C22#1684036112yes—
794C22#1684037612yes—
795C22#1684039412yes—
796C22D4×C22⋊D6112yes—
797C22#1684041112yes—
798C22#1684042012yes—
799C22#1684042012yes—
800C22#1684042512yes—
801C22#1684044212yes—
802C22#1684046612yes—
803C4—24no—
804C4—44no—
805C4—42no—
806C4—82no—
807C4—1224no—
808C4—1224no—
809C4—2444no—
810C4—2444no—
811C4—2442no—
812C2—44no—
813C2—2444no—
814C2#2144903611yescharacteristic
815C2#2144913011yescharacteristic
816C2#2144917711yescharacteristic
817C2#2144945011yescharacteristic
818C2#2144962412yes—
819C2#2144966412yes—
820C2#2144978212yes—
821C2#2144981612yes—
822C2#2145099611yescharacteristic
823C2#2145174211yescharacteristic
824C2#2145410311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutator, socle, cosocleC24×C61C24
FittingC2×C61×#393C2
prime radicalC23×C22⋊D61C22
hypercenterC2×#393D61
hypocenterC61#14723
LCSG ▷ C24×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#393

Complements

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

NH ≅ G/Ntype
1. C22×#14519753C2semidirect
3. C2×#16839681C2semidirect
4. C2×#16839634C2semidirect
5. #21444073C2semidirect
6. #21444064C2semidirect
7. #21444063C2semidirect
9. #21444050C2semidirect
10. #21444040C2semidirect
11. C2×C61×#393C2semidirect
50. C22×C22⋊D61Q8semidirect
78. C2×#11758196D4semidirect
251. C23×C61C22⋊Q8semidirect
343. C2×Dic61C22⋊Q8semidirect
403. C2×#393D61semidirect
455. C61#14723semidirect
687. C23#14519753semidirect

Maximal subgroups

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

subgroupindex
C22×#145197532
C22×#145197372
C2×#168396812
C2×#168396342
#214440732
#214440642
#214440632
#214440582
#214440502
#214440402
C2×C61×#3932
#1472361