Finite Group Databasebeta

← #29603139

Subgroups — #29603139

Order 15616.

2474 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×#14519761C211yesmaximal, characteristic
2C2×#16839641C211yesmaximal, characteristic
3C2×#16839639C211yesmaximal, characteristic
4C2×#16839623C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×Dic61C211yesmaximal, characteristic, complemented
6C22×#14519684C211yesmaximal, characteristic, complemented
7#21444088C212yesmaximal, complemented
8#21444061C212yesmaximal, complemented
9#21444055C212yesmaximal, complemented
10#21444048C212yesmaximal, complemented
11C2×C61×#385C211yesmaximal, characteristic, complemented
12C23×C22⋊D61C2211yescharacteristic
13C24×Dic61C2211yescharacteristic
14C24×Dic61C2211yescharacteristic
15C2×#14519761—24no—
16C2×#14519761—24no—
17C2×#14519761C418yescomplemented
18C22×C4⋊Dic61C2212yes—
19C22×C22⋊Dic61C2211yescharacteristic
20C22×#11758198C2211yescharacteristic
21C22×#11758198C2212yes—
22C22×#11758198C2212yes—
23C22×#11758198C2211yescharacteristic
24C22×C4×Dic61C2212yes—
25#16839641—24no—
26#16839639—24no—
27#16839623—24no—
28C22⋊C4×Dic61—24no—
29C2×#14519684—24no—
30C2×#14519684C2212yes—
31C2×#14519684C2212yes—
32C2×#14519684C2211yescharacteristic
33C2×#14519684C2211yescharacteristic
34C2×#14519684C2212yes—
35C2×#14519684C2212yes—
36C2×#14519684C2212yes—
37C2×#14519684C2212yes—
38C24×C4×C61C2211yescharacteristic
39C22×C4⋊C4×C61C2212yes—
40C22×C22⋊C4×C61C2211yescharacteristic
41C22×C22⋊C4×C61C2211yescharacteristic
42C61×#385—24no—
43C2×#95×C61C2212yes—
44C24×D61C2311yescharacteristic
45C22×C22⋊D61—22no—
46C22×C22⋊D61—22no—
47C22×C22⋊D61—22no—
48C22×C22⋊D61—22no—
49C22×C22⋊D61—22no—
50C22×C22⋊D61—22no—
51C22×C22⋊D61C2×C414yes—
52C23×Dic61—22no—
53C23×Dic61—22no—
54C23×Dic61—22no—
55C23×Dic61—22no—
56C23×Dic61—22no—
57C23×Dic61—22no—
58C23×Dic61—22no—
59C23×Dic61—22no—
60C23×Dic61—24no—
61C23×Dic61—42no—
62C23×Dic61C2×C414yes—
63C23×Dic61D414yes—
64C23×Dic61C2312yes—
65C23×Dic61C2311yescharacteristic
66C23×Dic61C2312yes—
67C23×Dic61C2311yescharacteristic
68C23×Dic61C2311yescharacteristic
69#14519761—232no—
70C2×C4⋊Dic61—24no—
71C2×C4⋊Dic61—24no—
72C2×C4⋊Dic61C2×C418yescomplemented
73C2×C22⋊Dic61—22no—
74C2×C22⋊Dic61—22no—
75C2×C22⋊Dic61D414yes—
76C2×#11758198—24no—
77C2×#11758198—24no—
78C2×#11758198—24no—
79C2×#11758198—22no—
80C2×#11758198—22no—
81C2×#11758198—24no—
82C2×#11758198—24no—
83C2×#11758198—42no—
84C2×#11758198—42no—
85C2×#11758198C2×C418yescomplemented
86C2×C4×Dic61—24no—
87C2×C4×Dic61—24no—
88C2×C4×Dic61—42no—
89#14519684—24no—
90#14519684—24no—
91#14519684—24no—
92#14519684—24no—
93#14519684—24no—
94#14519684—22no—
95#14519684—22no—
96#14519684—24no—
97C25×C61C2311yescharacteristic
98C23×C4×C61—22no—
99C23×C4×C61—24no—
100C23×C4×C61—22no—
101C23×C4×C61—22no—
102C23×C4×C61—42no—
103C23×C4×C61C2311yescharacteristic
104C23×C4×C61C2311yescharacteristic
105C23×C4×C61C2312yes—
106C23×C4×C61C2312yes—
107C2×C4⋊C4×C61—24no—
108C2×C4⋊C4×C61—24no—
109C2×C4⋊C4×C61—42no—
110C2×C22⋊C4×C61—22no—
111C2×C22⋊C4×C61—22no—
112C2×C22⋊C4×C61—22no—
113C2×C22⋊C4×C61C2×C414yes—
114C2×C22⋊C4×C61D414yes—
115C2×C22⋊C4×C61D414yes—
116#95×C61—24no—
117C24×C61—22no—
118C24×C61—22no—
119C24×C61—22no—
120C24×C61—22no—
121C24×C61C22×C412yes—
122C24×C61C2×D412yes—
123C24×C61C2×D412yes—
124C24×C61C2×D412yes—
125C24×C61C2×D412yes—
126C24×C61#4112yes—
127C24×C61#4112yes—
128C24×C61C2411yescharacteristic
129C23×D61—21no—
130C23×D61—21no—
131C23×D61—21no—
132C23×D61—21no—
133C23×D61—21no—
134C23×D61—21no—
135C23×D61—22no—
136C23×D61—22no—
137C23×D61—22no—
138C23×D61—22no—
139C23×D61C22×C412yes—
140C22×C4×C61—22no—
141C22×C4×C61—22no—
142C22×C4×C61—22no—
143C22×C4×C61—22no—
144C22×C4×C61—28no—
145C22×C4×C61—22no—
146C22×C4×C61—22no—
147C22×C4×C61—22no—
148C22×C4×C61—22no—
149C22×C4×C61—22no—
150C22×C4×C61—22no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—22no—
158C22×C4×C61—22no—
159C22×C4×C61—22no—
160C22×C4×C61—22no—
161C22×C4×C61—48no—
162C22×C4×C61—48no—
163C22×C4×C61—44no—
164C22×C4×C61—44no—
165C22×C4×C61C22×C414yes—
166C22×C4×C61C2×D414yes—
167C22×C4×C61C2×D414yes—
168C22×C4×C61#4114yes—
169C2×C22⋊D61—28no—
170C2×C22⋊D61—28no—
171C2×C22⋊D61—28no—
172C2×C22⋊D61—44no—
173C2×C22⋊D61—44no—
174C2×C22⋊D61—44no—
175C2×C22⋊D61—44no—
176C22×Dic61—21no—
177C22×Dic61—21no—
178C22×Dic61—22no—
179C22×Dic61—28no—
180C22×Dic61—28no—
181C22×Dic61—28no—
182C22×Dic61—28no—
183C22×Dic61—22no—
184C22×Dic61—22no—
185C22×Dic61—21no—
186C22×Dic61—22no—
187C22×Dic61—22no—
188C22×Dic61—21no—
189C22×Dic61—21no—
190C22×Dic61—21no—
191C22×Dic61—21no—
192C22×Dic61—22no—
193C22×Dic61—22no—
194C22×Dic61—22no—
195C22×Dic61—21no—
196C22×Dic61—22no—
197C22×Dic61—21no—
198C22×Dic61—21no—
199C22×Dic61—22no—
200C22×Dic61—22no—
201C22×Dic61—22no—
202C22×Dic61—22no—
203C22×Dic61—22no—
204C22×Dic61—22no—
205C22×Dic61—28no—
206C22×Dic61—44no—
207C22×Dic61—48no—
208C22×Dic61—48no—
209C22×Dic61—44no—
210C22×Dic61—44no—
211C22×Dic61—44no—
212C22×Dic61—44no—
213C22×Dic61C22×C414yes—
214C22×Dic61C22×C412yes—
215C22×Dic61C2×D412yes—
216C22×Dic61C2×D414yes—
217C22×Dic61C2×D412yes—
218C22×Dic61#4114yes—
219C4⋊C4×C61—48no—
220C22⋊C4×C61—44no—
221C22⋊C4×C61C22⋊C4116yescomplemented
222C22⋊Dic61—28no—
223#11758198—216no—
224#11758198—48no—
225#11758198—44no—
226#11758198—44no—
227C4⋊Dic61—216no—
228C4×Dic61—48no—
229C23×C61—24no—
230C23×C61—24no—
231C23×C61—22no—
232C23×C61—22no—
233C23×C61—24no—
234C23×C61—22no—
235C23×C61—22no—
236C23×C61—24no—
237C23×C61—24no—
238C23×C61—24no—
239C23×C61—24no—
240C23×C61—24no—
241C23×C61—24no—
242C23×C61—24no—
243C23×C61—24no—
244C23×C61—24no—
245C23×C61C2×C22⋊C414yes—
246C23×C61C4×D414yes—
247C23×C61C4×D414yes—
248C23×C61#12114yes—
249C23×C61#12114yes—
250C23×C61#12414yes—
251C23×C61#12714yes—
252C23×C61C23×C411yescharacteristic
253C23×C61C22×D411yescharacteristic
254C23×C61C22×D411yescharacteristic
255C23×C61C22×D411yescharacteristic
256C23×C61C22×D411yescharacteristic
257C23×C61C2×#4111yescharacteristic
258C23×C61C2×#4111yescharacteristic
259C23×C61C2×#4112yes—
260C23×C61C2×#4112yes—
261C23×C61H(5,𝔽2)12yes—
262C23×C612−1+412yes—
263C22×D61—22no—
264C22×D61—22no—
265C22×D61—22no—
266C22×D61—24no—
267C22×D61—24no—
268C22×D61—41no—
269C22×D61—41no—
270C22×D61—41no—
271C22×D61—41no—
272C22×D61—41no—
273C22×D61—42no—
274C22×D61—41no—
275C22×D61—41no—
276C22×D61—41no—
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×D61—42no—
286C2×C4×C61—24no—
287C2×C4×C61—24no—
288C2×C4×C61—24no—
289C2×C4×C61—24no—
290C2×C4×C61—24no—
291C2×C4×C61—24no—
292C2×C4×C61—24no—
293C2×C4×C61—24no—
294C2×C4×C61—24no—
295C2×C4×C61—416no—
296C2×C4×C61—42no—
297C2×C4×C61—42no—
298C2×C4×C61—42no—
299C2×C4×C61—42no—
300C2×C4×C61—41no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
303C2×C4×C61—41no—
304C2×C4×C61—41no—
305C2×C4×C61—41no—
306C2×C4×C61—42no—
307C2×C4×C61—42no—
308C2×C4×C61—42no—
309C2×C4×C61—42no—
310C2×C4×C61C2×C22⋊C418yes—
311C22⋊D61—416no—
312C2×Dic61—22no—
313C2×Dic61—22no—
314C2×Dic61—24no—
315C2×Dic61—24no—
316C2×Dic61—22no—
317C2×Dic61—24no—
318C2×Dic61—24no—
319C2×Dic61—24no—
320C2×Dic61—22no—
321C2×Dic61—22no—
322C2×Dic61—24no—
323C2×Dic61—22no—
324C2×Dic61—22no—
325C2×Dic61—22no—
326C2×Dic61—24no—
327C2×Dic61—24no—
328C2×Dic61—416no—
329C2×Dic61—42no—
330C2×Dic61—42no—
331C2×Dic61—41no—
332C2×Dic61—41no—
333C2×Dic61—42no—
334C2×Dic61—41no—
335C2×Dic61—42no—
336C2×Dic61—42no—
337C2×Dic61—41no—
338C2×Dic61—42no—
339C2×Dic61—42no—
340C2×Dic61—42no—
341C2×Dic61—42no—
342C2×Dic61—42no—
343C2×Dic61—416no—
344C2×Dic61#12314yescomplemented
345#13996—611nomaximal, Sylow
346C22×C61—24no—
347C22×C61—28no—
348C22×C61—28no—
349C22×C61—24no—
350C22×C61—24no—
351C22×C61—28no—
352C22×C61—28no—
353C22×C61—24no—
354C22×C61—24no—
355C22×C61—24no—
356C22×C61#39018yes—
357C22×C61C22×C22⋊C411yescharacteristic
358C22×C61C2×C4×D411yescharacteristic
359C22×C61C2×C4×D411yescharacteristic
360C22×C61C4×#4112yes—
361C22×C61#52012yes—
362C22×C61C2×#12111yescharacteristic
363C22×C61C2×#12111yescharacteristic
364C22×C61C2×#12311yescharacteristic
365C22×C61#52511yescharacteristic
366C22×C61C2×#12411yescharacteristic
367C22×C61#52912yes—
368C22×C61C2×#12711yescharacteristic
369C22×C61#53411yescharacteristic
370C22×C61#53611yescharacteristic
371C22×C61#53912yes—
372C22×C61#54612yes—
373C22×C61#54612yes—
374C22×C61#54612yes—
375C22×C61#54712yes—
376C22×C61#54712yes—
377C22×C61#54712yes—
378C22×C61#55112yes—
379C22×C61#55212yes—
380C2×D61—42no—
381C2×D61—44no—
382C2×D61—44no—
383C2×D61—42no—
384C2×D61—42no—
385C2×D61—81no—
386C2×D61—81no—
387C2×D61—82no—
388C2×D61—82no—
389C2×D61—81no—
390C2×D61—81no—
391C4×C61—28no—
392C4×C61—44no—
393C4×C61—81no—
394C4×C61—81no—
395Dic61—24no—
396Dic61—42no—
397Dic61—44no—
398Dic61—44no—
399Dic61—42no—
400C22×#123—611no—
401C2×#386—611no—
402C2×#386—611no—
403C2×#385D6111yescharacteristic, complemented
404C2×#381—611no—
405C2×C4×C22⋊C4—611no—
406C22×#95—611no—
407#1445—612no—
408#1439—612no—
409#1437—612no—
410C4⋊#95—612no—
411C2×C61—28no—
412C2×C61C2×#39011yescharacteristic
413C2×C61C4×#12311yescharacteristic
414C2×C61#232211yescharacteristic
415C2×C61#233912yes—
416C2×C61#235912yes—
417C2×C61#241211yescharacteristic
418C2×C61#241311yescharacteristic
419C2×C61#242512yes—
420C2×C61#248812yes—
421C2×C61#250111yescharacteristic
422C2×C61#253911yescharacteristic
423D61—82no—
424C23×D4—611no—
425C24×C4—611no—
426C24×C4—611no—
427C24×C4C2×D6111yescharacteristic
428C2×#123—618no—
429C2×#123—1224no—
430C2×#123—1224no—
431C22×C4⋊C4—612no—
432C22×C4⋊C4C2×D6112yes—
433C22×C22⋊C4—611no—
434C22×C22⋊C4—612no—
435C22×C22⋊C4—611no—
436C22×C22⋊C4—612no—
437C22×C22⋊C4—611no—
438C22×C22⋊C4C2×D6111yescharacteristic
439C22×C22⋊C4C2×D6111yescharacteristic
440C22×C42—612no—
441#386—1224no—
442#386—1224no—
443#385—24no—
444#381—1224no—
445C4×C22⋊C4—1224no—
446C2×#95—611no—
447C2×#95—612no—
448C2×#95—612no—
449C2×#95—612no—
450C2×#95—612no—
451C2×#95—612no—
452C2×#95—612no—
453C2×#95—611no—
454C2×#95—1224no—
455C2×#95C2×D6112yes—
456C61#1399611yescharacteristic, complemented, Sylow
457C25—611no—
458C25C22×D6111yescharacteristic
459C22×D4—614no—
460C22×D4—1222no—
461C22×D4—1222no—
462C22×D4—1222no—
463C22×D4—1222no—
464C22×D4—1222no—
465C22×D4—1222no—
466C23×C4—22no—
467C23×C4—24no—
468C23×C4—22no—
469C23×C4—22no—
470C23×C4—42no—
471C23×C4—611no—
472C23×C4—614no—
473C23×C4—612no—
474C23×C4—612no—
475C23×C4—611no—
476C23×C4—611no—
477C23×C4—614no—
478C23×C4—1224no—
479C23×C4—1222no—
480C23×C4—1222no—
481C23×C4—1222no—
482C23×C4—1222no—
483C23×C4—1222no—
484C23×C4—1222no—
485C23×C4—1222no—
486C23×C4—1222no—
487C23×C4—2442no—
488C23×C4C22×D6111yescharacteristic
489C23×C4C22×D6111yescharacteristic
490C23×C4C22×D6112yes—
491C23×C4C22×D6112yes—
492#123—12232no—
493C2×C4⋊C4—24no—
494C2×C4⋊C4—24no—
495C2×C4⋊C4—42no—
496C2×C4⋊C4—618no—
497C2×C4⋊C4—1224no—
498C2×C4⋊C4—1224no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—614no—
503C2×C22⋊C4—618no—
504C2×C22⋊C4—1222no—
505C2×C22⋊C4—1222no—
506C2×C22⋊C4—1224no—
507C2×C22⋊C4—1224no—
508C2×C22⋊C4—1224no—
509C2×C22⋊C4—1222no—
510C2×C22⋊C4—1222no—
511C2×C22⋊C4—1224no—
512C2×C22⋊C4—1224no—
513C2×C22⋊C4—2442no—
514C2×C22⋊C4—2442no—
515C2×C22⋊C4C4×D6114yes—
516C2×C22⋊C4D24414yes—
517C2×C22⋊C4C22⋊D6114yes—
518C2×C42—1224no—
519C2×C42—1224no—
520C2×C42—2442no—
521#95—24no—
522#95—1224no—
523#95—1224no—
524#95—1224no—
525#95—1224no—
526#95—1224no—
527#95—1222no—
528#95—1222no—
529#95—1224no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—612no—
535C24—1221no—
536C24—1221no—
537C24—1221no—
538C24—1221no—
539C24—1222no—
540C24—1222no—
541C24—1221no—
542C24—1221no—
543C24—1222no—
544C24—1222no—
545C24C2×C4×D6112yes—
546C24C2×D24412yes—
547C24D4×D6112yes—
548C24D4×D6112yes—
549C24#1175822612yes—
550C24#1175822612yes—
551C24C2×C22⋊D6112yes—
552C24C23×D6111yescharacteristic
553C2×D4—1228no—
554C2×D4—1228no—
555C2×D4—1228no—
556C2×D4—2444no—
557C2×D4—2444no—
558C2×D4—2444no—
559C2×D4—2444no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—28no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—48no—
582C22×C4—48no—
583C22×C4—44no—
584C22×C4—44no—
585C22×C4—612no—
586C22×C4—614no—
587C22×C4—614no—
588C22×C4—612no—
589C22×C4—614no—
590C22×C4—612no—
591C22×C4—1228no—
592C22×C4—1221no—
593C22×C4—1221no—
594C22×C4—1222no—
595C22×C4—1222no—
596C22×C4—1222no—
597C22×C4—1221no—
598C22×C4—1221no—
599C22×C4—1222no—
600C22×C4—1221no—
601C22×C4—1221no—
602C22×C4—1222no—
603C22×C4—1222no—
604C22×C4—1221no—
605C22×C4—1222no—
606C22×C4—1222no—
607C22×C4—1222no—
608C22×C4—1222no—
609C22×C4—1222no—
610C22×C4—1222no—
611C22×C4—1221no—
612C22×C4—1221no—
613C22×C4—1221no—
614C22×C4—1222no—
615C22×C4—1222no—
616C22×C4—1222no—
617C22×C4—1228no—
618C22×C4—1228no—
619C22×C4—1228no—
620C22×C4—1228no—
621C22×C4—2444no—
622C22×C4—2448no—
623C22×C4—2448no—
624C22×C4—2444no—
625C22×C4—2444no—
626C22×C4—2444no—
627C22×C4—2444no—
628C22×C4C2×C4×D6114yes—
629C22×C4C2×D24414yes—
630C22×C4#1175822414yes—
631C22×C4C2×C22⋊D6114yes—
632C4⋊C4—48no—
633C4⋊C4—12216no—
634C22⋊C4—44no—
635C22⋊C4—1228no—
636C22⋊C4—12216no—
637C22⋊C4—2448no—
638C22⋊C4—2444no—
639C22⋊C4—2444no—
640C22⋊C4#11758198116yescomplemented
641C42—2448no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—22no—
646C23—22no—
647C23—24no—
648C23—22no—
649C23—22no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—1222no—
659C23—1222no—
660C23—1222no—
661C23—1224no—
662C23—1224no—
663C23—2442no—
664C23—2441no—
665C23—2441no—
666C23—2441no—
667C23—2441no—
668C23—2441no—
669C23—2442no—
670C23—2441no—
671C23—2441no—
672C23—2441no—
673C23—2442no—
674C23—2442no—
675C23—2442no—
676C23—2442no—
677C23—2442no—
678C23—2442no—
679C23—2442no—
680C23—2442no—
681C23C2×#1175819814yes—
682C23#1451973914yes—
683C23#1451973914yes—
684C23#1451975214yes—
685C23#1451975214yes—
686C23#1451976614yes—
687C23#1451977314yes—
688C23C22×C4×D6111yescharacteristic
689C23C2×D4×D6111yescharacteristic
690C23C2×D4×D6111yescharacteristic
691C23C22×C22⋊D6111yescharacteristic
692C23C22×D24411yescharacteristic
693C23#41×D6112yes—
694C23C2×#1175822412yes—
695C23C2×#1175822611yescharacteristic
696C23C2×#1175822611yescharacteristic
697C23#1451982212yes—
698C23#1451982412yes—
699D4—24416no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—416no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—614no—
725C2×C4—1222no—
726C2×C4—1222no—
727C2×C4—1224no—
728C2×C4—1224no—
729C2×C4—1224no—
730C2×C4—1222no—
731C2×C4—1224no—
732C2×C4—1224no—
733C2×C4—1222no—
734C2×C4—1222no—
735C2×C4—1224no—
736C2×C4—1222no—
737C2×C4—1222no—
738C2×C4—1222no—
739C2×C4—1224no—
740C2×C4—1224no—
741C2×C4—24416no—
742C2×C4—2442no—
743C2×C4—2442no—
744C2×C4—2441no—
745C2×C4—2441no—
746C2×C4—2442no—
747C2×C4—2441no—
748C2×C4—2442no—
749C2×C4—2442no—
750C2×C4—2441no—
751C2×C4—2442no—
752C2×C4—2442no—
753C2×C4—2442no—
754C2×C4—2442no—
755C2×C4—24416no—
756C2×C4—2442no—
757C2×C4C2×#1175819818yes—
758C22—24no—
759C22—24no—
760C22—24no—
761C22—28no—
762C22—24no—
763C22—28no—
764C22—28no—
765C22—28no—
766C22—24no—
767C22—24no—
768C22—4881no—
769C22—4881no—
770C22—4882no—
771C22—4882no—
772C22—4881no—
773C22—4881no—
774C22—2442no—
775C22—2442no—
776C22—2444no—
777C22—2442no—
778C22—2444no—
779C22#1683966318yes—
780C22C22×#1175819811yescharacteristic
781C22C2×#1451973911yescharacteristic
782C22C2×#1451973911yescharacteristic
783C22C4×#1175822412yes—
784C22#1684024112yes—
785C22C2×#1451975211yescharacteristic
786C22C2×#1451975211yescharacteristic
787C22#123×D6111yescharacteristic
788C22#1684026811yescharacteristic
789C22C2×#1451976611yescharacteristic
790C22#1684029812yes—
791C22C2×#1451977311yescharacteristic
792C22#1684032211yescharacteristic
793C22#1684033411yescharacteristic
794C22#1684036112yes—
795C22#1684039912yes—
796C22#1684040612yes—
797C22#1684040712yes—
798C22#1684041012yes—
799C22#1684041112yes—
800C22#1684041612yes—
801C22#1684043912yes—
802C22#1684045412yes—
803C4—28no—
804C4—44no—
805C4—81no—
806C4—81no—
807C4—1224no—
808C4—2444no—
809C4—2442no—
810C4—2444no—
811C4—2442no—
812C2—28no—
813C2—4882no—
814C2C2×#1683966311yescharacteristic
815C2#2144833811yescharacteristic
816C2#2144848711yescharacteristic
817C2#2144864412yes—
818C2#2144880912yes—
819C2#2144921311yescharacteristic
820C2#2144922411yescharacteristic
821C2#2144936812yes—
822C2#2145015112yes—
823C2#2145028811yescharacteristic
824C2#2145074711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C61×#385C2
socle, cosocleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenterC2×#385D61
hypocenterC61#13996
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
4. C2×#16839623C2semidirect
5. C2×C22⋊C4×Dic61C2semidirect
6. C22×#14519684C2semidirect
7. #21444088C2semidirect
8. #21444061C2semidirect
9. #21444055C2semidirect
10. #21444048C2semidirect
11. C2×C61×#385C2semidirect
17. C2×#14519761C4semidirect
72. C2×C4⋊Dic61C2×C4semidirect
85. C2×#11758198C2×C4semidirect
221. C22⋊C4×C61C22⋊C4semidirect
344. C2×Dic61#123semidirect
403. C2×#385D61semidirect
456. C61#13996semidirect
640. C22⋊C4#11758198semidirect

Maximal subgroups

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

subgroupindex
C22×#145197612
C2×#168396412
C2×#168396392
C2×#168396232
C2×C22⋊C4×Dic612
C22×#145196842
#214440882
#214440612
#214440552
#214440482
C2×C61×#3852
#1399661