Finite Group Databasebeta

← #29683759

Subgroups — #29683759

Order 15616.

1658 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840307C211yesmaximal, characteristic
2C2×#16839734C214yesmaximal, complemented
3#21448221C211yesmaximal, characteristic, complemented
4C4×#14519733C211yesmaximal, characteristic, complemented
5#21446656C211yesmaximal, characteristic, complemented
6#21446655C211yesmaximal, characteristic, complemented
7#21446654C211yesmaximal, characteristic, complemented
8#21446653C214yesmaximal, complemented
9C61×#1964C211yesmaximal, characteristic, complemented
10C22×#11758224C2212yes—
11#16840307—21no—
12#16840307—21no—
13#16840307—21no—
14#16840307—21no—
15#16840307—21no—
16#16840307—21no—
17#16840307—21no—
18#16840307—21no—
19C2×#14519776C411yescharacteristic, complemented
20C2×#14519773C411yescharacteristic, complemented
21C2×#14519763C412yescomplemented
22C2×#14519751C2211yescharacteristic
23C2×#14519749C2212yes—
24C2×D4×Dic61C411yescharacteristic, complemented
25C2×#14519739C411yescharacteristic, complemented
26C2×#14519737C412yescomplemented
27C2×#14519733C2212yes—
28C2×#14519733C2212yes—
29C22×C4×Dic61C2211yescharacteristic
30#16839734—216no—
31C2×#14519692C2214yes—
32C2×#14519691C2214yes—
33C2×#14519691C2214yes—
34#16839631—21no—
35#16839626—21no—
36#16839622C2211yescharacteristic
37#16839620C2212yes—
38C4⋊C4×Dic61—21no—
39C4×#11758196—21no—
40#16839613—21no—
41#16839613—21no—
42C22⋊C4×Dic61C2212yes—
43C4×C22⋊Dic61C2211yescharacteristic
44#16839607—21no—
45C42×Dic61—21no—
46C2×#121×C61C2211yescharacteristic
47C2×#99×C61C2214yes—
48C61×#380C2211yescharacteristic
49C4×C22⋊C4×C61C2211yescharacteristic
50C2×#11758224—28no—
51C2×#11758224—22no—
52C2×#11758224—22no—
53C2×#11758224—22no—
54C2×#11758224—22no—
55C2×#11758224—28no—
56C22×Dic122C2×C412yes—
57C22×D244C2×C411yescharacteristic
58C22×C22⋊D61C2×C412yes—
59C22×C22⋊D61C2×C412yes—
60C22×C22⋊D61C2312yes—
61C23×Dic61C2×C412yes—
62C23×Dic61C2311yescharacteristic
63C23×Dic61C2311yescharacteristic
64C22×C4×D61C2×C412yes—
65#14519776—21no—
66#14519776—21no—
67#14519776—21no—
68#14519776—21no—
69#14519773—21no—
70#14519773—21no—
71#14519773—21no—
72#14519773—21no—
73#14519763—22no—
74#14519763—22no—
75#14519763—22no—
76#14519763—22no—
77#14519751—21no—
78#14519751—21no—
79#14519751—21no—
80#14519751—21no—
81#14519749—22no—
82#14519749—22no—
83#14519749—22no—
84#14519749—22no—
85D4×Dic61—21no—
86D4×Dic61—21no—
87D4×Dic61—21no—
88D4×Dic61—21no—
89#14519739—21no—
90#14519739—21no—
91#14519739—21no—
92#14519739—21no—
93#14519737—22no—
94#14519737—22no—
95#14519737—22no—
96#14519737—22no—
97#14519733—24no—
98#14519733—28no—
99#14519733D418yescomplemented
100C2×C4⋊Dic61—21no—
101C2×C4⋊Dic61C2×C411yescharacteristic
102C2×#11758196—22no—
103C2×#11758196—22no—
104C2×#11758196—22no—
105C2×#11758196C2×C412yes—
106C2×C22⋊Dic61C2×C412yes—
107C2×C22⋊Dic61C2312yes—
108C2×C22⋊Dic61C2312yes—
109C2×#11758198C2×C412yes—
110C2×#11758198C2×C412yes—
111C2×C4×Dic61—22no—
112C2×C4×Dic61—21no—
113C2×C4×Dic61—22no—
114C2×C4×Dic61—22no—
115C2×C4×Dic61C2×C411yescharacteristic
116C2×C4×Dic61C2×C411yescharacteristic
117C2×C4×Dic61C2×C411yescharacteristic
118C2×C4×Dic61C2×C411yescharacteristic
119C2×C4×Dic61D411yescharacteristic
120C2×C4×Dic61D411yescharacteristic
121C2×C4×Dic61D411yescharacteristic
122C2×C4×Dic61D411yescharacteristic
123C2×C4×Dic61D411yescharacteristic
124C2×C4×Dic61D411yescharacteristic
125C2×C4×Dic61D411yescharacteristic
126C2×C4×Dic61D411yescharacteristic
127#14519692—28no—
128#14519691—28no—
129#14519691—28no—
130#14519684—21no—
131#14519684—21no—
132#14519684—22no—
133#14519684—22no—
134C22×D4×C61C2×C411yescharacteristic
135C22×D4×C61C2312yes—
136C23×C4×C61C2311yescharacteristic
137#121×C61—21no—
138#121×C61—21no—
139#121×C61—21no—
140#121×C61—21no—
141C2×C4⋊C4×C61—21no—
142C2×C4⋊C4×C61C2×C411yescharacteristic
143C2×C22⋊C4×C61C2×C412yes—
144C2×C22⋊C4×C61C2312yes—
145C2×C22⋊C4×C61C2312yes—
146C2×C42×C61—21no—
147#99×C61—28no—
148#95×C61—21no—
149#95×C61—21no—
150C24×C61C22×C412yes—
151C24×C61C2411yescharacteristic
152C23×D61C22×C412yes—
153C2×D4×C61—24no—
154C2×D4×C61—22no—
155C2×D4×C61—22no—
156C2×D4×C61—24no—
157C2×D4×C61—21no—
158C2×D4×C61—21no—
159C2×D4×C61—42no—
160C22×C4×C61—22no—
161C22×C4×C61—22no—
162C22×C4×C61—42no—
163C22×C4×C61C22×C412yes—
164C22×C4×C61C22×C411yescharacteristic
165C22×C4×C61C22×C411yescharacteristic
166C22×C4×C61C2×D411yescharacteristic
167C22×C4×C61C2×D411yescharacteristic
168C22×C4×C61C2×D411yescharacteristic
169C22×C4×C61C2×D411yescharacteristic
170C2×C22⋊D61—24no—
171C2×C22⋊D61—22no—
172C2×C22⋊D61—22no—
173C2×C22⋊D61—24no—
174C2×C22⋊D61—22no—
175C2×C22⋊D61—22no—
176C2×C22⋊D61—22no—
177C2×C22⋊D61—22no—
178C2×C22⋊D61—28no—
179C2×C22⋊D61—44no—
180C22×Dic61—22no—
181C22×Dic61—22no—
182C22×Dic61—22no—
183C22×Dic61—28no—
184C22×Dic61—22no—
185C22×Dic61—42no—
186C22×Dic61C22×C412yes—
187C22×Dic61C22×C411yescharacteristic
188C22×Dic61C22×C411yescharacteristic
189C22×Dic61C22×C411yescharacteristic
190C22×Dic61C22×C411yescharacteristic
191C22×Dic61C2×D411yescharacteristic
192C22×Dic61C2×D411yescharacteristic
193C22×Dic61C2×D411yescharacteristic
194C22×Dic61C2×D411yescharacteristic
195C22×Dic61C2×D411yescharacteristic
196C22×Dic61C2×D411yescharacteristic
197C22×Dic61C2×D411yescharacteristic
198C22×Dic61C2×D411yescharacteristic
199C22×Dic61C2×D414yes—
200C22×Dic61#4114yes—
201#11758224—48no—
202#11758224—48no—
203#11758224—44no—
204#11758224—44no—
205#11758224—44no—
206#11758224—44no—
207C2×D244—21no—
208C2×D244—21no—
209C2×D244—42no—
210C2×C4×D61—22no—
211C2×C4×D61—22no—
212C2×C4×D61—28no—
213C2×Dic122—22no—
214C2×Dic122—22no—
215C2×Dic122—28no—
216C4⋊C4×C61—21no—
217C4⋊C4×C61—21no—
218C4⋊C4×C61—42no—
219C22⋊C4×C61—22no—
220C22⋊C4×C61—22no—
221C22⋊C4×C61—22no—
222C22⋊C4×C61—24no—
223C22⋊C4×C61C2×D414yes—
224C42×C61—42no—
225C22⋊Dic61—22no—
226C22⋊Dic61—22no—
227C22⋊Dic61—22no—
228C22⋊Dic61—24no—
229C22⋊Dic61C2×D414yes—
230#11758198—22no—
231#11758198—22no—
232#11758198—22no—
233#11758198—22no—
234C4⋊Dic61—21no—
235C4⋊Dic61—21no—
236C4⋊Dic61—42no—
237#11758196—22no—
238#11758196—22no—
239#11758196—28no—
240#11758196—44no—
241#11758196—44no—
242C4×Dic61—28no—
243C4×Dic61—44no—
244C4×Dic61—42no—
245C4×Dic61—44no—
246C4×Dic61C22⋊C411yescharacteristic
247C4×Dic61C22⋊C411yescharacteristic
248C4×Dic61C22⋊C411yescharacteristic
249C4×Dic61C22⋊C411yescharacteristic
250C4×Dic61C22⋊C411yescharacteristic
251C4×Dic61C22⋊C411yescharacteristic
252C4×Dic61C22⋊C411yescharacteristic
253C4×Dic61C22⋊C411yescharacteristic
254C4×Dic61C22⋊C411yescharacteristic
255C4×Dic61C22⋊C411yescharacteristic
256C4×Dic61C22⋊C411yescharacteristic
257C4×Dic61C22⋊C411yescharacteristic
258C4×Dic61C22⋊C411yescharacteristic
259C4×Dic61C22⋊C411yescharacteristic
260C4×Dic61C22⋊C411yescharacteristic
261C4×Dic61C22⋊C411yescharacteristic
262C23×C61—22no—
263C23×C61—24no—
264C23×C61—41no—
265C23×C61—41no—
266C23×C61—42no—
267C23×C61—42no—
268C23×C61C23×C411yescharacteristic
269C23×C61C22×D411yescharacteristic
270C23×C61C22×D411yescharacteristic
271C23×C61C22×D412yes—
272C23×C61C2×#4112yes—
273C22×D61—22no—
274C22×D61—24no—
275C22×D61—42no—
276C22×D61—42no—
277D4×C61—42no—
278D4×C61—44no—
279D4×C61—42no—
280D4×C61—42no—
281D4×C61—42no—
282C2×C4×C61—22no—
283C2×C4×C61—22no—
284C2×C4×C61—22no—
285C2×C4×C61—22no—
286C2×C4×C61—24no—
287C2×C4×C61—24no—
288C2×C4×C61—41no—
289C2×C4×C61—41no—
290C2×C4×C61—41no—
291C2×C4×C61—42no—
292C2×C4×C61—42no—
293C2×C4×C61—42no—
294C2×C4×C61—42no—
295C2×C4×C61—42no—
296C2×C4×C61C2×C22⋊C411yescharacteristic
297C2×C4×C61C2×C22⋊C411yescharacteristic
298C2×C4×C61C2×C22⋊C411yescharacteristic
299C2×C4×C61C2×C22⋊C411yescharacteristic
300C22⋊D61—44no—
301C22⋊D61—44no—
302C22⋊D61—42no—
303C22⋊D61—42no—
304C22⋊D61—44no—
305C22⋊D61—44no—
306C22⋊D61—44no—
307C2×Dic61—22no—
308C2×Dic61—22no—
309C2×Dic61—22no—
310C2×Dic61—22no—
311C2×Dic61—24no—
312C2×Dic61—24no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61—42no—
317C2×Dic61—42no—
318C2×Dic61—44no—
319C2×Dic61—44no—
320C2×Dic61—42no—
321C2×Dic61—42no—
322C2×Dic61—42no—
323C2×Dic61C2×C22⋊C411yescharacteristic
324C2×Dic61C2×C22⋊C411yescharacteristic
325C2×Dic61C2×C22⋊C411yescharacteristic
326C2×Dic61C2×C22⋊C411yescharacteristic
327C2×Dic61C2×C22⋊C411yescharacteristic
328C2×Dic61C2×C22⋊C411yescharacteristic
329C2×Dic61C2×C22⋊C411yescharacteristic
330C2×Dic61C2×C22⋊C411yescharacteristic
331C2×Dic61C4×D414yes—
332C2×Dic61C4×D414yes—
333C2×Dic61#12114yes—
334C2×Dic61#12114yes—
335C2×Dic61#12412yes—
336C2×Dic61#12412yes—
337C2×Dic61#12712yes—
338C2×Dic61#12712yes—
339D244—42no—
340D244—42no—
341C4×D61—44no—
342C4×D61—44no—
343Dic122—44no—
344Dic122—44no—
345#21212—611nomaximal, Sylow
346C22×C61—21no—
347C22×C61—21no—
348C22×C61—21no—
349C22×C61—21no—
350C22×C61—21no—
351C22×C61—21no—
352C22×C61—42no—
353C22×C61—42no—
354C22×C61—42no—
355C22×C61—42no—
356C22×C61—42no—
357C22×C61—84no—
358C22×C61C22×C22⋊C411yescharacteristic
359C22×C61C2×C4×D412yes—
360C22×C61C2×#12112yes—
361C22×C61C2×#12411yescharacteristic
362C22×C61C2×#12711yescharacteristic
363C2×D61—42no—
364C2×D61—42no—
365C2×D61—42no—
366C2×D61—84no—
367C4×C61—21no—
368C4×C61—21no—
369C4×C61—21no—
370C4×C61—44no—
371C4×C61—42no—
372C4×C61—82no—
373C4×C61#41012yescomplemented
374Dic61—21no—
375Dic61—21no—
376Dic61—21no—
377Dic61—44no—
378Dic61—42no—
379Dic61—82no—
380Dic61#39012yes—
381Dic61#39012yes—
382Dic61#39012yes—
383Dic61#39012yes—
384Dic61#41012yescomplemented
385C2×#532—611no—
386C2×#410—614no—
387#2285—611no—
388C4×#117—611no—
389#1964—614no—
390#1964—611no—
391#1964—611no—
392#1964—611no—
393#1964D6111yescharacteristic, complemented
394C2×C61—22no—
395C2×C61—21no—
396C2×C61—22no—
397C2×C61—21no—
398C2×C61—82no—
399C2×C61C2×#39011yescharacteristic
400C2×C61C2×#41011yescharacteristic
401C2×C61C2×#41011yescharacteristic
402D61—82no—
403C22×#41—612no—
404#532—1221no—
405#532—1221no—
406#532—1221no—
407#532—1221no—
408#532—1221no—
409#532—1221no—
410#532—1221no—
411#532—1221no—
412C2×C4⋊Q8—611no—
413C2×#127—611no—
414C2×#124—612no—
415C2×#121—612no—
416C2×#121—611no—
417C2×#121C2×D6111yescharacteristic
418C2×C4×D4—611no—
419C2×C4×D4—611no—
420C2×C4×D4—612no—
421C2×#117—612no—
422C2×#117—612no—
423C22×C42—611no—
424#410—12216no—
425C2×#99—614no—
426C2×#99—614no—
427C2×#99—614no—
428C2×#99C2×D6114yes—
429#384—1221no—
430#382—1221no—
431#380—611no—
432#380—612no—
433#380C2×D6111yescharacteristic
434C4×C4⋊C4—1221no—
435C4×C4⋊C4—1221no—
436C4×C4⋊C4—1221no—
437C4×C4⋊C4—1221no—
438C4×C22⋊C4—611no—
439C4×C22⋊C4—612no—
440C4×C22⋊C4C2×D6111yescharacteristic
441#376—1221no—
442C43—1221no—
443C61#2121211yescharacteristic, complemented, Sylow
444C2×#41—1222no—
445C2×#41—1222no—
446C2×#41—1222no—
447C2×#41—1222no—
448C2×#41—1228no—
449C2×#41—1228no—
450C22×Q8—612no—
451C22×D4—612no—
452C22×D4—612no—
453C22×D4—612no—
454C22×D4—611no—
455C22×D4C4×D6111yescharacteristic
456C22×D4C22×D6112yes—
457C23×C4—611no—
458C23×C4—611no—
459C23×C4—612no—
460C23×C4—612no—
461C23×C4C22×D6111yescharacteristic
462C4⋊Q8—1221no—
463C4⋊Q8—1221no—
464C4⋊Q8—1221no—
465C4⋊Q8—1221no—
466#127—1221no—
467#127—1221no—
468#127—1221no—
469#127—1221no—
470#124—1222no—
471#124—1222no—
472#124—1222no—
473#124—1222no—
474#121—21no—
475#121—21no—
476#121—21no—
477#121—21no—
478#121—1222no—
479#121—1222no—
480#121—1222no—
481#121—1222no—
482#121—1221no—
483#121—1221no—
484#121—1221no—
485#121—1221no—
486C4×D4—1222no—
487C4×D4—1222no—
488C4×D4—1222no—
489C4×D4—1222no—
490C4×D4—1221no—
491C4×D4—1221no—
492C4×D4—1221no—
493C4×D4—1221no—
494C4×D4—1221no—
495C4×D4—1221no—
496C4×D4—1221no—
497C4×D4—1221no—
498#117—618no—
499#117—1224no—
500#117—1228no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—612no—
503C2×C4⋊C4—611no—
504C2×C4⋊C4—1222no—
505C2×C4⋊C4—1222no—
506C2×C4⋊C4—1222no—
507C2×C4⋊C4—1221no—
508C2×C4⋊C4C4×D6111yescharacteristic
509C2×C22⋊C4—612no—
510C2×C22⋊C4—612no—
511C2×C22⋊C4—612no—
512C2×C22⋊C4—612no—
513C2×C22⋊C4—612no—
514C2×C22⋊C4C4×D6112yes—
515C2×C22⋊C4C22×D6112yes—
516C2×C22⋊C4C22×D6112yes—
517C2×C42—21no—
518C2×C42—611no—
519C2×C42—611no—
520C2×C42—611no—
521C2×C42—611no—
522C2×C42—611no—
523C2×C42—611no—
524C2×C42—611no—
525C2×C42—611no—
526C2×C42—611no—
527C2×C42—611no—
528C2×C42—611no—
529C2×C42—611no—
530C2×C42—1222no—
531C2×C42—1222no—
532C2×C42—1222no—
533C2×C42—1221no—
534#99—28no—
535#99—1228no—
536#99—1228no—
537#99—1228no—
538#95—21no—
539#95—21no—
540#95—1222no—
541#95—1222no—
542#95—1221no—
543#95—1221no—
544C24—612no—
545C24C2×C4×D6112yes—
546C24C23×D6111yescharacteristic
547#41—2448no—
548#41—2448no—
549#41—2444no—
550#41—2444no—
551#41—2444no—
552#41—2444no—
553C2×Q8—1222no—
554C2×Q8—1222no—
555C2×Q8—1228no—
556C2×D4—24no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—24no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—42no—
563C2×D4—1222no—
564C2×D4—1222no—
565C2×D4—1222no—
566C2×D4—1222no—
567C2×D4—1228no—
568C2×D4—1224no—
569C2×D4—1222no—
570C2×D4—1222no—
571C2×D4—1224no—
572C2×D4—1221no—
573C2×D4—1221no—
574C2×D4—2442no—
575C2×D4—2444no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—42no—
579C22×C4—611no—
580C22×C4—611no—
581C22×C4—611no—
582C22×C4—611no—
583C22×C4—611no—
584C22×C4—611no—
585C22×C4—614no—
586C22×C4—614no—
587C22×C4—611no—
588C22×C4—611no—
589C22×C4—611no—
590C22×C4—611no—
591C22×C4—611no—
592C22×C4—611no—
593C22×C4—612no—
594C22×C4—1222no—
595C22×C4—1222no—
596C22×C4—1228no—
597C22×C4—1222no—
598C22×C4—1222no—
599C22×C4—1228no—
600C22×C4—1222no—
601C22×C4—1222no—
602C22×C4—2442no—
603C22×C4C2×C4×D6112yes—
604C22×C4C2×C4×D6111yescharacteristic
605C22×C4C2×C4×D6111yescharacteristic
606C22×C4D4×D6111yescharacteristic
607C22×C4D4×D6111yescharacteristic
608C22×C4D4×D6111yescharacteristic
609C22×C4D4×D6111yescharacteristic
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—42no—
613C4⋊C4—1222no—
614C4⋊C4—1222no—
615C4⋊C4—1228no—
616C4⋊C4—1221no—
617C4⋊C4—1221no—
618C4⋊C4—2442no—
619C4⋊C4—2444no—
620C4⋊C4—2444no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—24no—
625C22⋊C4—614no—
626C22⋊C4—1222no—
627C22⋊C4—1222no—
628C22⋊C4—1222no—
629C22⋊C4—1222no—
630C22⋊C4—1222no—
631C22⋊C4—1222no—
632C22⋊C4—1222no—
633C22⋊C4—1224no—
634C22⋊C4D4×D6114yes—
635C42—42no—
636C42—611no—
637C42—611no—
638C42—611no—
639C42—611no—
640C42—611no—
641C42—611no—
642C42—611no—
643C42—611no—
644C42—611no—
645C42—611no—
646C42—611no—
647C42—611no—
648C42—611no—
649C42—611no—
650C42—611no—
651C42—611no—
652C42—1228no—
653C42—2442no—
654C42—2444no—
655C42—2444no—
656C23—22no—
657C23—24no—
658C23—41no—
659C23—41no—
660C23—42no—
661C23—42no—
662C23—1224no—
663C23—1222no—
664C23—2442no—
665C23—2442no—
666C23C22×C4×D6111yescharacteristic
667C23C2×D4×D6111yescharacteristic
668C23C2×D4×D6111yescharacteristic
669C23C2×D4×D6112yes—
670C23#41×D6112yes—
671Q8—2444no—
672Q8—2444no—
673D4—42no—
674D4—44no—
675D4—42no—
676D4—42no—
677D4—42no—
678D4—2442no—
679D4—2444no—
680D4—2444no—
681D4—2444no—
682D4—2444no—
683D4—2444no—
684D4—2442no—
685D4—2442no—
686D4—2442no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—611no—
702C2×C4—611no—
703C2×C4—611no—
704C2×C4—611no—
705C2×C4—611no—
706C2×C4—614no—
707C2×C4—614no—
708C2×C4—614no—
709C2×C4—614no—
710C2×C4—612no—
711C2×C4—612no—
712C2×C4—612no—
713C2×C4—612no—
714C2×C4—611no—
715C2×C4—611no—
716C2×C4—611no—
717C2×C4—1222no—
718C2×C4—1222no—
719C2×C4—1222no—
720C2×C4—1222no—
721C2×C4—1224no—
722C2×C4—1224no—
723C2×C4—2444no—
724C2×C4—2444no—
725C2×C4—2444no—
726C2×C4—2444no—
727C2×C4—2441no—
728C2×C4—2441no—
729C2×C4—2441no—
730C2×C4—2442no—
731C2×C4—2442no—
732C2×C4—2442no—
733C2×C4—2442no—
734C2×C4—2442no—
735C2×C4C22⋊C4×D6111yescharacteristic
736C2×C4C22⋊C4×D6111yescharacteristic
737C2×C4C22⋊C4×D6111yescharacteristic
738C2×C4C22⋊C4×D6111yescharacteristic
739C22—21no—
740C22—21no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—21no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—84no—
751C22—4884no—
752C22—2442no—
753C22—2442no—
754C22—2442no—
755C22C2×C22⋊C4×D6111yescharacteristic
756C22C4×D4×D6112yes—
757C22#121×D6112yes—
758C22#124×D6111yescharacteristic
759C22#127×D6111yescharacteristic
760C4—21no—
761C4—21no—
762C4—21no—
763C4—44no—
764C4—42no—
765C4—82no—
766C4—612no—
767C4—612no—
768C4—612no—
769C4—612no—
770C4—612no—
771C4—1221no—
772C4—1221no—
773C4—1221no—
774C4—4882no—
775C4—2444no—
776C4—2442no—
777C4#1683973412yescomplemented
778C2—22no—
779C2—21no—
780C2—22no—
781C2—21no—
782C2—82no—
783C2—4882no—
784C2#390×D6111yescharacteristic
785C2#410×D6111yescharacteristic
786C2C2×#1683973411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC61×#1964C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840307C2
cosocleC24×C61C24
hypercenter#1964D61
hypocenterC61#21212
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1964

Complements

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

NH ≅ G/Ntype
2. C2×#16839734C2semidirect
3. #21448221C2semidirect
4. C4×#14519733C2semidirect
5. #21446656C2semidirect
6. #21446655C2semidirect
7. #21446654C2semidirect
8. #21446653C2semidirect
9. C61×#1964C2semidirect
19. C2×#14519776C4semidirect
20. C2×#14519773C4semidirect
21. C2×#14519763C4semidirect
24. C2×D4×Dic61C4semidirect
25. C2×#14519739C4semidirect
26. C2×#14519737C4semidirect
99. #14519733D4semidirect
373. C4×C61#410semidirect
384. Dic61#410semidirect
393. #1964D61semidirect
443. C61#21212semidirect
777. C4#16839734semidirect

Maximal subgroups

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

subgroupindex
C2×#168403072
C2×#168397342
#214482212
C4×#145197332
#214466562
#214466552
#214466542
#214466532
C61×#19642
#2121261