Finite Group Databasebeta

← #29606404

Subgroups — #29606404

Order 15616.

2098 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839641C211yesmaximal, characteristic
2C2×#16839639C211yesmaximal, characteristic
3C2×#16839639C211yesmaximal, characteristic
4C22×#14519684C211yesmaximal, characteristic, complemented
5#21444080C212yesmaximal, complemented
6#21444078C212yesmaximal, complemented
7#21444067C212yesmaximal, complemented
8#21444061C212yesmaximal, complemented
9#21444041C211yesmaximal, characteristic, complemented
10#21444041C211yesmaximal, characteristic, complemented
11C2×C61×#385C211yesmaximal, characteristic, complemented
12C23×C22⋊D61C2211yescharacteristic
13C24×Dic61C2211yescharacteristic
14C24×Dic61C2211yescharacteristic
15C22×C22⋊Dic61C2211yescharacteristic
16C22×#11758198C2211yescharacteristic
17C22×#11758198C2211yescharacteristic
18C22×#11758198C2212yes—
19C22×#11758198C2212yes—
20#16839641—24no—
21#16839639—24no—
22#16839639C418yescomplemented
23C2×#14519684—24no—
24C2×#14519684C2211yescharacteristic
25C2×#14519684C2211yescharacteristic
26C2×#14519684C2212yes—
27C2×#14519684C2212yes—
28C2×#14519684C2212yes—
29C2×#14519684C2212yes—
30C2×#14519684C2212yes—
31C2×#14519684C2212yes—
32C2×#14519684C2212yes—
33C2×#14519684C2212yes—
34C24×C4×C61C2211yescharacteristic
35C22×C4⋊C4×C61C2212yes—
36C22×C22⋊C4×C61C2211yescharacteristic
37C22×C22⋊C4×C61C2211yescharacteristic
38C61×#385—24no—
39C2×#95×C61C2212yes—
40C24×D61C2311yescharacteristic
41C22×C22⋊D61—22no—
42C22×C22⋊D61—22no—
43C22×C22⋊D61—22no—
44C22×C22⋊D61—22no—
45C22×C22⋊D61—22no—
46C22×C22⋊D61—22no—
47C22×C22⋊D61C2×C414yes—
48C23×Dic61—22no—
49C23×Dic61—22no—
50C23×Dic61—22no—
51C23×Dic61—22no—
52C23×Dic61—42no—
53C23×Dic61—42no—
54C23×Dic61—42no—
55C23×Dic61—42no—
56C23×Dic61C2×C414yes—
57C23×Dic61D414yes—
58C23×Dic61C2312yes—
59C23×Dic61C2312yes—
60C23×Dic61C2311yescharacteristic
61C23×Dic61C2311yescharacteristic
62C23×Dic61C2311yescharacteristic
63C2×C22⋊Dic61—22no—
64C2×C22⋊Dic61—22no—
65C2×C22⋊Dic61—22no—
66C2×#11758198—24no—
67C2×#11758198—22no—
68C2×#11758198—22no—
69C2×#11758198—42no—
70C2×#11758198—42no—
71C2×#11758198—42no—
72C2×#11758198—42no—
73C2×#11758198—42no—
74C2×#11758198—42no—
75C2×#11758198C2×C418yescomplemented
76#14519684—24no—
77#14519684—24no—
78#14519684—24no—
79#14519684—22no—
80#14519684—22no—
81#14519684—42no—
82#14519684—42no—
83#14519684—42no—
84#14519684—42no—
85#14519684C2×C418yescomplemented
86C25×C61C2311yescharacteristic
87C23×C4×C61—22no—
88C23×C4×C61—22no—
89C23×C4×C61—42no—
90C23×C4×C61—42no—
91C23×C4×C61D414yes—
92C23×C4×C61C2311yescharacteristic
93C23×C4×C61C2311yescharacteristic
94C23×C4×C61C2312yes—
95C23×C4×C61C2312yes—
96C2×C4⋊C4×C61—24no—
97C2×C4⋊C4×C61—42no—
98C2×C4⋊C4×C61—42no—
99C2×C22⋊C4×C61—22no—
100C2×C22⋊C4×C61—22no—
101C2×C22⋊C4×C61—22no—
102C2×C22⋊C4×C61—22no—
103C2×C22⋊C4×C61—22no—
104C2×C22⋊C4×C61C2×C414yes—
105#95×C61—24no—
106C24×C61—22no—
107C24×C61—22no—
108C24×C61—22no—
109C24×C61—22no—
110C24×C61C22×C412yes—
111C24×C61C2×D412yes—
112C24×C61C2×D412yes—
113C24×C61#4112yes—
114C24×C61#4112yes—
115C24×C61#4112yes—
116C24×C61#4112yes—
117C24×C61C2411yescharacteristic
118C23×D61—21no—
119C23×D61—21no—
120C23×D61—21no—
121C23×D61—21no—
122C23×D61—21no—
123C23×D61—21no—
124C23×D61—22no—
125C23×D61—22no—
126C23×D61—22no—
127C23×D61—22no—
128C23×D61C22×C412yes—
129C22×C4×C61—28no—
130C22×C4×C61—22no—
131C22×C4×C61—22no—
132C22×C4×C61—22no—
133C22×C4×C61—22no—
134C22×C4×C61—22no—
135C22×C4×C61—22no—
136C22×C4×C61—22no—
137C22×C4×C61—22no—
138C22×C4×C61—22no—
139C22×C4×C61—22no—
140C22×C4×C61—22no—
141C22×C4×C61—22no—
142C22×C4×C61—21no—
143C22×C4×C61—21no—
144C22×C4×C61—21no—
145C22×C4×C61—21no—
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C22×C4×C61—22no—
149C22×C4×C61—22no—
150C22×C4×C61—22no—
151C22×C4×C61—22no—
152C22×C4×C61—48no—
153C22×C4×C61—44no—
154C22×C4×C61—44no—
155C22×C4×C61—48no—
156C22×C4×C61C22×C414yes—
157C22×C4×C61C2×D414yes—
158C2×C22⋊D61—28no—
159C2×C22⋊D61—28no—
160C2×C22⋊D61—28no—
161C2×C22⋊D61—44no—
162C2×C22⋊D61—44no—
163C2×C22⋊D61—44no—
164C2×C22⋊D61—44no—
165C22×Dic61—28no—
166C22×Dic61—28no—
167C22×Dic61—22no—
168C22×Dic61—21no—
169C22×Dic61—21no—
170C22×Dic61—22no—
171C22×Dic61—21no—
172C22×Dic61—21no—
173C22×Dic61—21no—
174C22×Dic61—21no—
175C22×Dic61—21no—
176C22×Dic61—21no—
177C22×Dic61—21no—
178C22×Dic61—21no—
179C22×Dic61—22no—
180C22×Dic61—22no—
181C22×Dic61—22no—
182C22×Dic61—22no—
183C22×Dic61—22no—
184C22×Dic61—22no—
185C22×Dic61—22no—
186C22×Dic61—22no—
187C22×Dic61—22no—
188C22×Dic61—22no—
189C22×Dic61—22no—
190C22×Dic61—22no—
191C22×Dic61—22no—
192C22×Dic61—22no—
193C22×Dic61—22no—
194C22×Dic61—48no—
195C22×Dic61—44no—
196C22×Dic61—44no—
197C22×Dic61—44no—
198C22×Dic61—44no—
199C22×Dic61—48no—
200C22×Dic61—48no—
201C22×Dic61—48no—
202C22×Dic61C22×C414yes—
203C22×Dic61C22×C412yes—
204C22×Dic61C2×D412yes—
205C22×Dic61C2×D412yes—
206C4⋊C4×C61—48no—
207C22⋊C4×C61—28no—
208C22⋊C4×C61—44no—
209C22⋊Dic61—44no—
210#11758198—48no—
211#11758198—44no—
212#11758198—44no—
213#11758198—48no—
214C23×C61—24no—
215C23×C61—24no—
216C23×C61—22no—
217C23×C61—22no—
218C23×C61—24no—
219C23×C61—22no—
220C23×C61—22no—
221C23×C61—24no—
222C23×C61—24no—
223C23×C61—24no—
224C23×C61—24no—
225C23×C61—24no—
226C23×C61—24no—
227C23×C61—24no—
228C23×C61—24no—
229C23×C61—24no—
230C23×C61#11714yes—
231C23×C61C4×D414yes—
232C23×C61C4×D414yes—
233C23×C61#12114yes—
234C23×C61#12314yes—
235C23×C61#12414yes—
236C23×C61#12614yes—
237C23×C61C23×C411yescharacteristic
238C23×C61C22×D411yescharacteristic
239C23×C61C22×D411yescharacteristic
240C23×C61C2×#4111yescharacteristic
241C23×C61C2×#4111yescharacteristic
242C23×C61C2×#4111yescharacteristic
243C23×C61C2×#4111yescharacteristic
244C23×C61H(5,𝔽2)12yes—
245C23×C61H(5,𝔽2)12yes—
246C23×C61H(5,𝔽2)12yes—
247C23×C612−1+412yes—
248C22×D61—22no—
249C22×D61—22no—
250C22×D61—22no—
251C22×D61—24no—
252C22×D61—24no—
253C22×D61—41no—
254C22×D61—41no—
255C22×D61—41no—
256C22×D61—41no—
257C22×D61—41no—
258C22×D61—41no—
259C22×D61—42no—
260C22×D61—41no—
261C22×D61—41no—
262C22×D61—42no—
263C22×D61—42no—
264C22×D61—42no—
265C22×D61—42no—
266C22×D61—42no—
267C22×D61—42no—
268C22×D61—42no—
269C22×D61—42no—
270C22×D61—42no—
271C2×C4×C61—24no—
272C2×C4×C61—24no—
273C2×C4×C61—24no—
274C2×C4×C61—24no—
275C2×C4×C61—24no—
276C2×C4×C61—24no—
277C2×C4×C61—416no—
278C2×C4×C61—42no—
279C2×C4×C61—42no—
280C2×C4×C61—42no—
281C2×C4×C61—42no—
282C2×C4×C61—42no—
283C2×C4×C61—42no—
284C2×C4×C61—42no—
285C2×C4×C61—42no—
286C2×C4×C61—41no—
287C2×C4×C61—41no—
288C2×C4×C61—41no—
289C2×C4×C61—41no—
290C2×C4×C61—42no—
291C2×C4×C61—41no—
292C2×C4×C61—41no—
293C2×C4×C61—42no—
294C2×C4×C61—42no—
295C2×C4×C61—42no—
296C22⋊D61—416no—
297C2×Dic61—22no—
298C2×Dic61—24no—
299C2×Dic61—22no—
300C2×Dic61—22no—
301C2×Dic61—24no—
302C2×Dic61—24no—
303C2×Dic61—22no—
304C2×Dic61—22no—
305C2×Dic61—22no—
306C2×Dic61—22no—
307C2×Dic61—22no—
308C2×Dic61—22no—
309C2×Dic61—416no—
310C2×Dic61—416no—
311C2×Dic61—41no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—42no—
316C2×Dic61—42no—
317C2×Dic61—42no—
318C2×Dic61—42no—
319C2×Dic61—42no—
320C2×Dic61—42no—
321C2×Dic61—42no—
322C2×Dic61—42no—
323C2×Dic61—42no—
324C2×Dic61—42no—
325C2×Dic61—42no—
326C2×Dic61—42no—
327C2×Dic61—42no—
328C2×Dic61—42no—
329C2×Dic61—42no—
330#14259—611nomaximal, Sylow
331C22×C61—28no—
332C22×C61—24no—
333C22×C61—24no—
334C22×C61—28no—
335C22×C61—24no—
336C22×C61—24no—
337C22×C61—24no—
338C22×C61—24no—
339C22×C61—28no—
340C22×C61—28no—
341C22×C61#38818yes—
342C22×C61C2×#11711yescharacteristic
343C22×C61C2×C4×D411yescharacteristic
344C22×C61C2×C4×D411yescharacteristic
345C22×C61#51812yes—
346C22×C61#52012yes—
347C22×C61C2×#12111yescharacteristic
348C22×C61C2×#12311yescharacteristic
349C22×C61C2×#12411yescharacteristic
350C22×C61C2×#12611yescharacteristic
351C22×C61#53412yes—
352C22×C61#53411yescharacteristic
353C22×C61#53411yescharacteristic
354C22×C61#53511yescharacteristic
355C22×C61#53611yescharacteristic
356C22×C61#53712yes—
357C22×C61#53812yes—
358C22×C61#53812yes—
359C22×C61#53812yes—
360C22×C61#53812yes—
361C22×C61#53912yes—
362C22×C61#53912yes—
363C22×C61#53912yes—
364C22×C61#53912yes—
365C2×D61—44no—
366C2×D61—42no—
367C2×D61—42no—
368C2×D61—44no—
369C2×D61—42no—
370C2×D61—81no—
371C2×D61—81no—
372C2×D61—81no—
373C2×D61—81no—
374C2×D61—82no—
375C2×D61—82no—
376C4×C61—44no—
377C4×C61—44no—
378C4×C61—81no—
379C4×C61—81no—
380Dic61—44no—
381Dic61—42no—
382Dic61—42no—
383Dic61—42no—
384Dic61—82no—
385C2×#386—611no—
386C2×#386—611no—
387C2×#386—611no—
388C2×#385D6111yescharacteristic, complemented
389C22×#95—611no—
390#1443—612no—
391#1442—612no—
392#1440—612no—
393#1439—612no—
394C22⋊#95—611no—
395C22⋊#95—611no—
396C2×C61—28no—
397C2×C61C2×#38811yescharacteristic
398C2×C61#231812yes—
399C2×C61#232111yescharacteristic
400C2×C61#232211yescharacteristic
401C2×C61#232512yes—
402C2×C61#261711yescharacteristic
403C2×C61#261811yescharacteristic
404C2×C61#262211yescharacteristic
405C2×C61#262311yescharacteristic
406C2×C61#263912yes—
407C2×C61#264312yes—
408D61—82no—
409C23×D4—611no—
410C24×C4—611no—
411C24×C4—611no—
412C24×C4C2×D6111yescharacteristic
413C22×C4⋊C4C2×D6112yes—
414C22×C22⋊C4—612no—
415C22×C22⋊C4—611no—
416C22×C22⋊C4—611no—
417C22×C22⋊C4—612no—
418C22×C22⋊C4—611no—
419C22×C22⋊C4C2×D6111yescharacteristic
420C22×C22⋊C4C2×D6111yescharacteristic
421#386—618no—
422#386—1224no—
423#386—1224no—
424#385—24no—
425C2×#95—612no—
426C2×#95—612no—
427C2×#95—612no—
428C2×#95—611no—
429C2×#95—612no—
430C2×#95—611no—
431C2×#95—612no—
432C2×#95—612no—
433C2×#95—612no—
434C2×#95—612no—
435C2×#95—1224no—
436C2×#95C2×D6112yes—
437C61#1425911yescharacteristic, complemented, Sylow
438C25—611no—
439C25C22×D6111yescharacteristic
440C22×D4—614no—
441C22×D4—1222no—
442C22×D4—1222no—
443C22×D4—1222no—
444C22×D4—1222no—
445C22×D4—1222no—
446C22×D4—1222no—
447C23×C4—22no—
448C23×C4—22no—
449C23×C4—42no—
450C23×C4—42no—
451C23×C4—612no—
452C23×C4—611no—
453C23×C4—611no—
454C23×C4—611no—
455C23×C4—614no—
456C23×C4—614no—
457C23×C4—612no—
458C23×C4—1222no—
459C23×C4—1222no—
460C23×C4—1222no—
461C23×C4—1222no—
462C23×C4—2442no—
463C23×C4—2442no—
464C23×C4—2442no—
465C23×C4—2442no—
466C23×C4C22⋊D6114yes—
467C23×C4C22×D6111yescharacteristic
468C23×C4C22×D6111yescharacteristic
469C23×C4C22×D6112yes—
470C23×C4C22×D6112yes—
471C2×C4⋊C4—24no—
472C2×C4⋊C4—42no—
473C2×C4⋊C4—42no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—618no—
480C2×C22⋊C4—1222no—
481C2×C22⋊C4—1222no—
482C2×C22⋊C4—1222no—
483C2×C22⋊C4—1222no—
484C2×C22⋊C4—1222no—
485C2×C22⋊C4—1224no—
486C2×C22⋊C4—2442no—
487C2×C22⋊C4—2442no—
488C2×C22⋊C4—2442no—
489C2×C22⋊C4—2442no—
490C2×C22⋊C4—2442no—
491C2×C22⋊C4—2442no—
492C2×C22⋊C4C4×D6114yes—
493#95—24no—
494#95—618no—
495#95—1224no—
496#95—1224no—
497#95—1222no—
498#95—1222no—
499#95—1224no—
500#95—2442no—
501#95—2442no—
502#95—2442no—
503#95—2442no—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24—612no—
509C24—1221no—
510C24—1221no—
511C24—1221no—
512C24—1221no—
513C24—1221no—
514C24—1221no—
515C24—1222no—
516C24—1222no—
517C24—1222no—
518C24—1222no—
519C24C2×C4×D6112yes—
520C24#1175822212yes—
521C24D4×D6112yes—
522C24#1175822412yes—
523C24#1175822612yes—
524C24#1175822612yes—
525C24C2×C22⋊D6112yes—
526C24C23×D6111yescharacteristic
527C2×D4—1228no—
528C2×D4—1228no—
529C2×D4—1228no—
530C2×D4—2444no—
531C2×D4—2444no—
532C2×D4—2444no—
533C2×D4—2444no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—28no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—48no—
558C22×C4—44no—
559C22×C4—44no—
560C22×C4—48no—
561C22×C4—612no—
562C22×C4—614no—
563C22×C4—612no—
564C22×C4—612no—
565C22×C4—1222no—
566C22×C4—1221no—
567C22×C4—1221no—
568C22×C4—1221no—
569C22×C4—1221no—
570C22×C4—1221no—
571C22×C4—1221no—
572C22×C4—1222no—
573C22×C4—1221no—
574C22×C4—1221no—
575C22×C4—1221no—
576C22×C4—1221no—
577C22×C4—1222no—
578C22×C4—1222no—
579C22×C4—1222no—
580C22×C4—1222no—
581C22×C4—1222no—
582C22×C4—1222no—
583C22×C4—1222no—
584C22×C4—1222no—
585C22×C4—1228no—
586C22×C4—1228no—
587C22×C4—1222no—
588C22×C4—1222no—
589C22×C4—1222no—
590C22×C4—1222no—
591C22×C4—1222no—
592C22×C4—1222no—
593C22×C4—1222no—
594C22×C4—2448no—
595C22×C4—2444no—
596C22×C4—2444no—
597C22×C4—2444no—
598C22×C4—2444no—
599C22×C4—2448no—
600C22×C4—2448no—
601C22×C4—2448no—
602C22×C4C2×C4×D6114yes—
603C22×C4C2×C22⋊D6114yes—
604C4⋊C4—48no—
605C22⋊C4—28no—
606C22⋊C4—44no—
607C22⋊C4—2448no—
608C22⋊C4—2448no—
609C22⋊C4—2444no—
610C22⋊C4—2444no—
611C22⋊C4—2444no—
612C23—24no—
613C23—24no—
614C23—24no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—24no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—24no—
626C23—24no—
627C23—24no—
628C23—1222no—
629C23—1222no—
630C23—1222no—
631C23—1224no—
632C23—1224no—
633C23—2441no—
634C23—2441no—
635C23—2441no—
636C23—2441no—
637C23—2442no—
638C23—2441no—
639C23—2441no—
640C23—2441no—
641C23—2441no—
642C23—2442no—
643C23—2442no—
644C23—2442no—
645C23—2442no—
646C23—2442no—
647C23—2442no—
648C23—2442no—
649C23—2442no—
650C23—2442no—
651C23#1451973514yes—
652C23C4×C22⋊D6114yes—
653C23#1451973914yes—
654C23#1451974914yes—
655C23#1451976214yes—
656C23#1451976614yes—
657C23#1451977214yes—
658C23C22×C4×D6111yescharacteristic
659C23C2×D4×D6111yescharacteristic
660C23C22×C22⋊D6111yescharacteristic
661C23C2×#1175822411yescharacteristic
662C23C2×#1175822211yescharacteristic
663C23C2×#1175822611yescharacteristic
664C23C2×#1175822611yescharacteristic
665C23#1451982212yes—
666C23#1451982212yes—
667C23#1451982312yes—
668C23#1451982412yes—
669D4—24416no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—416no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—42no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—1222no—
696C2×C4—1222no—
697C2×C4—1224no—
698C2×C4—1222no—
699C2×C4—1224no—
700C2×C4—1224no—
701C2×C4—1222no—
702C2×C4—1222no—
703C2×C4—1222no—
704C2×C4—1222no—
705C2×C4—1222no—
706C2×C4—1222no—
707C2×C4—2442no—
708C2×C4—2442no—
709C2×C4—2442no—
710C2×C4—2442no—
711C2×C4—2442no—
712C2×C4—2442no—
713C2×C4—2442no—
714C2×C4—24416no—
715C2×C4—24416no—
716C2×C4—2441no—
717C2×C4—2441no—
718C2×C4—2441no—
719C2×C4—2441no—
720C2×C4—2442no—
721C2×C4—2442no—
722C2×C4—2442no—
723C2×C4—2442no—
724C2×C4—2442no—
725C2×C4—2442no—
726C2×C4—2442no—
727C2×C4—2442no—
728C22—24no—
729C22—24no—
730C22—24no—
731C22—24no—
732C22—28no—
733C22—24no—
734C22—24no—
735C22—28no—
736C22—28no—
737C22—28no—
738C22—4881no—
739C22—4881no—
740C22—4881no—
741C22—4881no—
742C22—4882no—
743C22—4882no—
744C22—2442no—
745C22—2442no—
746C22—2442no—
747C22—2444no—
748C22—2444no—
749C22#1683965218yes—
750C22C2×#1451973511yescharacteristic
751C22C2×C4×C22⋊D6111yescharacteristic
752C22C2×#1451973911yescharacteristic
753C22#1684023412yes—
754C22#1684024112yes—
755C22C2×#1451974911yescharacteristic
756C22C2×#1451976211yescharacteristic
757C22C2×#1451976611yescharacteristic
758C22C2×#1451977211yescharacteristic
759C22#1684032112yes—
760C22#1684032211yescharacteristic
761C22#1684032311yescharacteristic
762C22#1684032711yescharacteristic
763C22#1684033411yescharacteristic
764C22#1684034012yes—
765C22#1684034512yes—
766C22#1684034712yes—
767C22#1684035212yes—
768C22#1684035212yes—
769C22#1684035412yes—
770C22#1684035612yes—
771C22#1684036112yes—
772C22#1684036112yes—
773C4—44no—
774C4—44no—
775C4—81no—
776C4—81no—
777C4—4882no—
778C4—2444no—
779C4—2442no—
780C4—2442no—
781C4—2442no—
782C2—28no—
783C2—4882no—
784C2C2×#1683965211yescharacteristic
785C2#2144844712yes—
786C2#2144847611yescharacteristic
787C2#2144848711yescharacteristic
788C2#2144851712yes—
789C2#2145155711yescharacteristic
790C2#2145156511yescharacteristic
791C2#2145159711yescharacteristic
792C2#2145160511yescharacteristic
793C2#2145175312yes—
794C2#2145177512yes—
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C61×#385C2
socle, cosocleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenterC2×#385D61
hypocenterC61#14259
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
4. C22×#14519684C2semidirect
5. #21444080C2semidirect
6. #21444078C2semidirect
7. #21444067C2semidirect
8. #21444061C2semidirect
9. #21444041C2semidirect
10. #21444041C2semidirect
11. C2×C61×#385C2semidirect
22. #16839639C4semidirect
75. C2×#11758198C2×C4semidirect
85. #14519684C2×C4semidirect
388. C2×#385D61semidirect
437. C61#14259semidirect

Maximal subgroups

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

subgroupindex
C2×#168396412
C2×#168396392
C22×#145196842
#214440802
#214440782
#214440672
#214440612
#214440412
C2×C61×#3852
#1425961