Finite Group Databasebeta

← #29723933

Subgroups — #29723933

Order 15616.

1148 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839913C211yesmaximal, characteristic
2C2×C4×#11758200C211yesmaximal, characteristic, complemented
3#21449322C211yesmaximal, characteristic, complemented
4#21447340C211yesmaximal, characteristic, complemented
5#21447256C211yesmaximal, characteristic, complemented
6#21447136C211yesmaximal, characteristic, complemented
7#21447022C211yesmaximal, characteristic, complemented
8#21446505C211yesmaximal, characteristic, complemented
9#21446427C211yesmaximal, characteristic, complemented
10#21446177C211yesmaximal, characteristic, complemented
11#21446153C211yesmaximal, characteristic, complemented
12#21446066C211yesmaximal, characteristic, complemented
13#21445829C211yesmaximal, characteristic, complemented
14#21445750C211yesmaximal, characteristic
15D4×C22⋊C4×C61C211yesmaximal, characteristic
16C22×#11758200C2211yescharacteristic
17C22×#11758200C2211yescharacteristic
18C2×#14519756C2211yescharacteristic
19C2×C4×Dic122C2211yescharacteristic, complemented
20#16839913—24no—
21C4×#11758200—24no—
22C2×#14519710C2211yescharacteristic, complemented
23C2×#14519708C2211yescharacteristic, complemented
24C2×C4⋊#92418C2211yescharacteristic, complemented
25C2×#14519700C2211yescharacteristic, complemented
26C2×#14519700C2211yescharacteristic, complemented
27C2×#14519698C2211yescharacteristic
28C2×#14519698C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519698C2211yescharacteristic
32C2×#14519698C2211yescharacteristic
33C2×C22⋊#92418C2211yescharacteristic
34C2×C22⋊#92418C2211yescharacteristic
35C2×C4×#92418C2211yescharacteristic, complemented
36#16839703—21no—
37#16839690—21no—
38#16839668C2211yescharacteristic, complemented
39#16839660C2211yescharacteristic, complemented
40#16839656—21no—
41#16839644—21no—
42#16839628C2211yescharacteristic, complemented
43#16839622C2211yescharacteristic
44#16839524C2211yescharacteristic, complemented
45#16839524C2211yescharacteristic, complemented
46#16839524C2211yescharacteristic, complemented
47#16839524C2211yescharacteristic, complemented
48#16839517C2211yescharacteristic, complemented
49#16839517C2211yescharacteristic, complemented
50C23×D4×C61C2211yescharacteristic
51C2×C4×D4×C61C2211yescharacteristic
52C2×C4×D4×C61C2211yescharacteristic
53C22×C22⋊C4×C61—21no—
54C61×#390C2211yescharacteristic
55C61×#390C2211yescharacteristic
56C61×#386—21no—
57C61×#386—21no—
58C61×#380C2211yescharacteristic
59C61×#379—21no—
60C4×C22⋊C4×C61C2211yescharacteristic
61C22×Dic122C2311yescharacteristic
62C2×#11758200—22no—
63C2×#11758200—22no—
64C2×#11758200—22no—
65C2×#11758200—22no—
66C2×#11758200—41no—
67C2×#11758200D414yes—
68C22×#92418C2311yescharacteristic
69C22×#92418C2311yescharacteristic
70C22×#92418C2311yescharacteristic
71C22×#92418C2311yescharacteristic
72#14519756—22no—
73#14519756—41no—
74C4×Dic122—22no—
75C4×Dic122—41no—
76C2×C4⋊Dic61C2311yescharacteristic
77C2×C4⋊Dic61C2311yescharacteristic
78C2×C4⋊Dic61C2311yescharacteristic
79C2×#11758196—21no—
80C2×#11758196—21no—
81C2×#11758196—21no—
82C2×C22⋊Dic61—21no—
83C2×C22⋊Dic61—21no—
84C2×C4×Dic61—21no—
85#14519710—41no—
86#14519708—22no—
87C4⋊#92418—41no—
88#14519700—22no—
89#14519700—41no—
90#14519698—22no—
91#14519698—22no—
92#14519698—22no—
93#14519698—22no—
94#14519698—22no—
95#14519698—41no—
96C22⋊#92418—22no—
97C22⋊#92418—41no—
98C4×#92418—22no—
99#14519684—21no—
100#14519684—21no—
101#14519684—21no—
102#14519684—21no—
103#14519684—21no—
104#14519684—21no—
105C25×C61—21no—
106C22×D4×C61—22no—
107C22×D4×C61—22no—
108C22×D4×C61—22no—
109C22×D4×C61—22no—
110C22×D4×C61—21no—
111C22×D4×C61—41no—
112C22×D4×C61—41no—
113C22×D4×C61C2311yescharacteristic
114C22×D4×C61C2311yescharacteristic
115C23×C4×C61—21no—
116C23×C4×C61—21no—
117C23×C4×C61C2311yescharacteristic
118C4×D4×C61—22no—
119C4×D4×C61—22no—
120C4×D4×C61—41no—
121C4×D4×C61—41no—
122C2×C4⋊C4×C61C2311yescharacteristic
123C2×C4⋊C4×C61C2311yescharacteristic
124C2×C22⋊C4×C61—21no—
125C2×C22⋊C4×C61—21no—
126C2×C22⋊C4×C61—21no—
127C2×C22⋊C4×C61—21no—
128C2×C22⋊C4×C61—21no—
129C2×C22⋊C4×C61—21no—
130C2×C22⋊C4×C61—21no—
131C2×C22⋊C4×C61—44no—
132C2×C22⋊C4×C61D411yescharacteristic
133C2×C22⋊C4×C61D411yescharacteristic
134C2×C42×C61C2311yescharacteristic
135C2×C42×C61C2311yescharacteristic
136#95×C61—21no—
137#95×C61D411yescharacteristic
138#95×C61D411yescharacteristic
139C24×C61—21no—
140C24×C61—24no—
141C24×C61—21no—
142C24×C61—42no—
143C24×C61—42no—
144C24×C61—42no—
145C24×C61—42no—
146C24×C61—81no—
147C24×C61—81no—
148C24×C61C2×D411yescharacteristic
149C2×D4×C61—24no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61—42no—
159C2×D4×C61—42no—
160C2×D4×C61—44no—
161C2×D4×C61—44no—
162C2×D4×C61—44no—
163C2×D4×C61—44no—
164C2×D4×C61C2×D412yes—
165C2×D4×C61#4112yes—
166C2×D4×C61#4112yes—
167C2×D4×C61#4112yes—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—42no—
177C22×C4×C61—42no—
178C22×C4×C61—42no—
179C22×C4×C61—42no—
180C22×C4×C61—81no—
181C22×C4×C61—81no—
182C22×C4×C61C2×D411yescharacteristic
183C22×C4×C61C2×D411yescharacteristic
184C22×C4×C61C2×D411yescharacteristic
185C22×C4×C61C2×D411yescharacteristic
186C22×C4×C61C2×D411yescharacteristic
187C22×C4×C61C2411yescharacteristic
188C22×Dic61—21no—
189C22×Dic61—21no—
190C22×Dic61—21no—
191C22×Dic61—21no—
192C2×Dic122—21no—
193C2×Dic122—21no—
194C2×Dic122—21no—
195C2×Dic122—21no—
196C2×Dic122—21no—
197C2×Dic122C2×D412yes—
198C4⋊C4×C61—21no—
199C4⋊C4×C61—21no—
200C4⋊C4×C61—21no—
201C4⋊C4×C61—21no—
202C22⋊C4×C61—22no—
203C22⋊C4×C61—22no—
204C22⋊C4×C61—42no—
205C22⋊C4×C61—42no—
206C22⋊C4×C61—42no—
207C22⋊C4×C61—42no—
208C22⋊C4×C61—42no—
209C22⋊C4×C61—81no—
210C22⋊C4×C61—81no—
211C42×C61—21no—
212C42×C61—21no—
213C42×C61—21no—
214C42×C61—21no—
215C22⋊Dic61—42no—
216C22⋊Dic61—42no—
217#11758200—28no—
218#11758200—44no—
219C4⋊Dic61—21no—
220C4⋊Dic61—21no—
221C4⋊Dic61—21no—
222C4⋊Dic61—21no—
223C4⋊Dic61—21no—
224C4⋊Dic61—21no—
225#11758196—42no—
226#11758196—42no—
227#11758196—42no—
228C4×Dic61—42no—
229C2×#92418—21no—
230C2×#92418—21no—
231C2×#92418—21no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418C2×D412yes—
241C23×C61—21no—
242C23×C61—22no—
243C23×C61—21no—
244C23×C61—22no—
245C23×C61—22no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—22no—
251C23×C61—48no—
252C23×C61—48no—
253C23×C61—41no—
254C23×C61—41no—
255C23×C61—41no—
256C23×C61—41no—
257C23×C61—41no—
258C23×C61—41no—
259C23×C61—41no—
260C23×C61—41no—
261C23×C61—41no—
262C23×C61—41no—
263C23×C61—84no—
264C23×C61—84no—
265C23×C61—84no—
266C23×C61—84no—
267C23×C61—84no—
268C23×C61#13512yes—
269C23×C61C22×D411yescharacteristic
270D4×C61—22no—
271D4×C61—22no—
272D4×C61—22no—
273D4×C61—22no—
274D4×C61—22no—
275D4×C61—48no—
276D4×C61—41no—
277D4×C61—41no—
278D4×C61#12314yes—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—21no—
283C2×C4×C61—21no—
284C2×C4×C61—21no—
285C2×C4×C61—21no—
286C2×C4×C61—21no—
287C2×C4×C61—21no—
288C2×C4×C61—21no—
289C2×C4×C61—21no—
290C2×C4×C61—21no—
291C2×C4×C61—21no—
292C2×C4×C61—21no—
293C2×C4×C61—41no—
294C2×C4×C61—41no—
295C2×C4×C61—41no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61—41no—
299C2×C4×C61—41no—
300C2×C4×C61—41no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
303C2×C4×C61—84no—
304C2×C4×C61—84no—
305C2×C4×C61AGL(1,ℤ/8)12yes—
306C2×C4×C61C22×D411yescharacteristic
307C2×C4×C61C2×#4111yescharacteristic
308C2×C4×C61C2×#4111yescharacteristic
309C2×C4×C61C2×#4111yescharacteristic
310C2×C4×C61H(5,𝔽2)11yescharacteristic
311C2×C4×C61H(5,𝔽2)11yescharacteristic
312C2×Dic61—22no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61—41no—
317C2×Dic61—41no—
318C2×Dic61—41no—
319C2×Dic61—41no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324Dic122—22no—
325Dic122—22no—
326Dic122—41no—
327Dic122—41no—
328#92418—22no—
329#92418—41no—
330#92418—41no—
331#92418—41no—
332#24905—611nomaximal, Sylow
333C22×C61—22no—
334C22×C61—24no—
335C22×C61—22no—
336C22×C61—22no—
337C22×C61—42no—
338C22×C61—41no—
339C22×C61—42no—
340C22×C61—41no—
341C22×C61—42no—
342C22×C61—41no—
343C22×C61—42no—
344C22×C61—42no—
345C22×C61—42no—
346C22×C61—41no—
347C22×C61—42no—
348C22×C61—42no—
349C22×C61—42no—
350C22×C61—816no—
351C22×C61—81no—
352C22×C61—81no—
353C22×C61—81no—
354C22×C61—81no—
355C22×C61#52511yescharacteristic
356C22×C61D4211yescharacteristic
357C22×C61#54611yescharacteristic
358C22×C61C2×#13511yescharacteristic
359C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
360C22×C61#57711yescharacteristic
361C22×C61#57711yescharacteristic
362C4×C61—22no—
363C4×C61—41no—
364C4×C61—41no—
365C4×C61—41no—
366C4×C61—41no—
367C4×C61—81no—
368C4×C61—81no—
369C4×C61C2×#12311yescharacteristic
370C4×C61#53811yescharacteristic
371C4×C61#54611yescharacteristic
372C4×C61#55111yescharacteristic
373Dic61—42no—
374Dic61—81no—
375Dic61—81no—
376Dic61—81no—
377C2×#450—611no—
378C2×C4×SD16—611no—
379#2421—611no—
380D4×C22⋊C4D6111yescharacteristic
381#2092—611no—
382#2077—611no—
383#2055—611no—
384#2036—611no—
385#1934—611no—
386#1923—611no—
387#1880—611no—
388#1877—611no—
389#1862—611no—
390#1804—611no—
391#1786—611no—
392C2×C61—42no—
393C2×C61—44no—
394C2×C61—82no—
395C2×C61#241811yescharacteristic
396C2×C61#310511yescharacteristic
397C2×C61#312311yescharacteristic
398C2×C61#326511yescharacteristic
399C2×C61#328211yescharacteristic
400C2×C61#329611yescharacteristic
401C2×C61#332411yescharacteristic
402C23×D4C2×D6111yescharacteristic
403C22×SD16—611no—
404C22×SD16—611no—
405C2×C22⋊Q8—611no—
406C2×C4×Q8—611no—
407C2×C4×D4C2×D6111yescharacteristic
408C2×C4×D4C2×D6111yescharacteristic
409C22×C22⋊C4—21no—
410#450—1224no—
411C4×SD16—1224no—
412C2×#107—611no—
413C2×#106—611no—
414C2×C4⋊C8—611no—
415C2×#103—611no—
416C2×#103—611no—
417C2×#102—611no—
418C2×#102—611no—
419C2×#102—611no—
420C2×#102—611no—
421C2×#102—611no—
422C2×#102—611no—
423C2×C22⋊C8—611no—
424C2×C22⋊C8—611no—
425C2×C4×C8—611no—
426#400—1221no—
427#397—1221no—
428#391—611no—
429#390C2×D6111yescharacteristic
430#390C2×D6111yescharacteristic
431#389—611no—
432#388—1221no—
433#387—1221no—
434#386—21no—
435#386—21no—
436#382—611no—
437#380—611no—
438#380C2×D6111yescharacteristic
439#379—21no—
440C4×C22⋊C4C2×D6111yescharacteristic
441#340—611no—
442#340—611no—
443#340—611no—
444#340—611no—
445#336—611no—
446#336—611no—
447C61#2490511yescharacteristic, complemented, Sylow
448C25—21no—
449C22×Q8—611no—
450C22×D4—22no—
451C22×D4—22no—
452C22×D4—22no—
453C22×D4—22no—
454C22×D4—21no—
455C22×D4—41no—
456C22×D4—41no—
457C22×D4C22×D6111yescharacteristic
458C22×D4C22×D6111yescharacteristic
459C23×C4—21no—
460C23×C4—21no—
461C23×C4C22×D6111yescharacteristic
462C2×SD16—614no—
463C2×SD16—1222no—
464C2×SD16—1222no—
465C2×SD16—1222no—
466C2×SD16—1222no—
467C2×SD16—2441no—
468C22×C8—611no—
469C22×C8—611no—
470C22×C8—611no—
471C22×C8—611no—
472C22⋊Q8—1222no—
473C22⋊Q8—2441no—
474C4×Q8—1222no—
475C4×Q8—2441no—
476C4×D4—22no—
477C4×D4—22no—
478C4×D4—41no—
479C4×D4—41no—
480C2×C4⋊C4—611no—
481C2×C4⋊C4—611no—
482C2×C4⋊C4—611no—
483C2×C4⋊C4—1221no—
484C2×C4⋊C4—1221no—
485C2×C4⋊C4—1221no—
486C2×C4⋊C4C22×D6111yescharacteristic
487C2×C4⋊C4C22×D6111yescharacteristic
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—44no—
496C2×C22⋊C4—1221no—
497C2×C22⋊C4—1221no—
498C2×C22⋊C4C22⋊D6111yescharacteristic
499C2×C22⋊C4C22⋊D6111yescharacteristic
500C2×C42—1221no—
501C2×C42C22×D6111yescharacteristic
502C2×C42C22×D6111yescharacteristic
503#107—2441no—
504#106—1222no—
505C4⋊C8—2441no—
506#103—1222no—
507#103—2441no—
508#102—1222no—
509#102—1222no—
510#102—1222no—
511#102—1222no—
512#102—1222no—
513#102—2441no—
514C22⋊C8—1222no—
515C22⋊C8—2441no—
516C4×C8—1222no—
517#95—21no—
518#95—1221no—
519#95—1221no—
520#95—1221no—
521#95—1221no—
522#95—1221no—
523#95—1221no—
524#95C22⋊D6111yescharacteristic
525#95C22⋊D6111yescharacteristic
526C24—21no—
527C24—24no—
528C24—21no—
529C24—42no—
530C24—42no—
531C24—42no—
532C24—42no—
533C24—81no—
534C24—81no—
535C24C2×C22⋊D6111yescharacteristic
536C2×Q8—612no—
537C2×Q8—1221no—
538C2×Q8—1221no—
539C2×Q8—1221no—
540C2×Q8—1221no—
541C2×Q8—1221no—
542C2×D4—24no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—42no—
552C2×D4—42no—
553C2×D4—44no—
554C2×D4—44no—
555C2×D4—44no—
556C2×D4—44no—
557C2×D4#1175822212yes—
558C2×D4#1175822212yes—
559C2×D4D4×D6112yes—
560C2×D4#1175822412yes—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—81no—
574C22×C4—81no—
575C22×C4—1221no—
576C22×C4—1221no—
577C22×C4—1221no—
578C22×C4—1221no—
579C22×C4C2×C22⋊D6111yescharacteristic
580C22×C4C2×C22⋊D6111yescharacteristic
581C22×C4C2×C22⋊D6111yescharacteristic
582C22×C4C2×C22⋊D6111yescharacteristic
583C22×C4C2×C22⋊D6111yescharacteristic
584C22×C4C23×D6111yescharacteristic
585SD16—1228no—
586SD16—2444no—
587C2×C8—612no—
588C2×C8—1221no—
589C2×C8—1221no—
590C2×C8—1221no—
591C2×C8—1221no—
592C2×C8—1221no—
593C2×C8—1221no—
594C2×C8—1221no—
595C2×C8—1221no—
596C2×C8—1221no—
597C2×C8—1221no—
598C2×C8—1221no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—1221no—
604C4⋊C4—1221no—
605C4⋊C4—1221no—
606C4⋊C4—1221no—
607C4⋊C4—1221no—
608C4⋊C4—1221no—
609C4⋊C4—2442no—
610C4⋊C4—2442no—
611C4⋊C4—2442no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—42no—
615C22⋊C4—42no—
616C22⋊C4—42no—
617C22⋊C4—42no—
618C22⋊C4—42no—
619C22⋊C4—81no—
620C22⋊C4—81no—
621C22⋊C4—2442no—
622C22⋊C4—2442no—
623C42—21no—
624C42—21no—
625C42—21no—
626C42—21no—
627C42—2442no—
628C23—21no—
629C23—22no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—22no—
634C23—21no—
635C23—22no—
636C23—21no—
637C23—22no—
638C23—48no—
639C23—48no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—84no—
651C23—84no—
652C23—84no—
653C23—84no—
654C23—84no—
655C23#1451979712yes—
656C23C22×C22⋊D6111yescharacteristic
657Q8—1222no—
658Q8—1222no—
659Q8—2441no—
660Q8—2441no—
661D4—22no—
662D4—22no—
663D4—22no—
664D4—22no—
665D4—22no—
666D4—48no—
667D4—41no—
668D4—41no—
669D4#1451975914yes—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—84no—
695C2×C4—84no—
696C2×C4—1222no—
697C2×C4—2441no—
698C2×C4—2441no—
699C2×C4—2441no—
700C2×C4—2441no—
701C2×C4—2441no—
702C2×C4—2441no—
703C2×C4—2441no—
704C2×C4—2441no—
705C2×C4—2441no—
706C2×C4—2441no—
707C2×C4—2441no—
708C2×C4#1451980312yes—
709C2×C4C2×D4×D6111yescharacteristic
710C2×C4C2×#1175822411yescharacteristic
711C2×C4C2×#1175822211yescharacteristic
712C2×C4C2×#1175822211yescharacteristic
713C2×C4#1451982211yescharacteristic
714C2×C4#1451982211yescharacteristic
715C8—1222no—
716C8—2441no—
717C8—2441no—
718C8—2441no—
719C22—24no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—41no—
724C22—42no—
725C22—42no—
726C22—41no—
727C22—42no—
728C22—41no—
729C22—41no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—816no—
737C22—81no—
738C22—81no—
739C22—81no—
740C22—81no—
741C22#1684027311yescharacteristic
742C22D4×C22⋊D6111yescharacteristic
743C22#1684040611yescharacteristic
744C22C2×#1451979711yescharacteristic
745C22C2×#1451980311yescharacteristic
746C22#1684057311yescharacteristic
747C22#1684057311yescharacteristic
748C4—22no—
749C4—41no—
750C4—41no—
751C4—41no—
752C4—41no—
753C4—81no—
754C4—81no—
755C4—4881no—
756C4—4881no—
757C4—4881no—
758C4—2442no—
759C4C2×#1451975911yescharacteristic
760C4#1684035011yescharacteristic
761C4#1684040211yescharacteristic
762C4#1684043811yescharacteristic
763C2—42no—
764C2—44no—
765C2—82no—
766C2#2144928111yescharacteristic
767C2#2145586611yescharacteristic
768C2#2145607111yescharacteristic
769C2#2145731011yescharacteristic
770C2#2145752211yescharacteristic
771C2#2145765411yescharacteristic
772C2#2145805011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingD4×C22⋊C4×C61C2
socleC23×C61C22×D4
prime radicalC23×D4×C61C22
hypercenterD4×C22⋊C4D61
hypocenterC61#24905
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11758200C2semidirect
3. #21449322C2semidirect
4. #21447340C2semidirect
5. #21447256C2semidirect
6. #21447136C2semidirect
7. #21447022C2semidirect
8. #21446505C2semidirect
9. #21446427C2semidirect
10. #21446177C2semidirect
11. #21446153C2semidirect
12. #21446066C2semidirect
13. #21445829C2semidirect
19. C2×C4×Dic122C22semidirect
22. C2×#14519710C22semidirect
23. C2×#14519708C22semidirect
24. C2×C4⋊#92418C22semidirect
25. C2×#14519700C22semidirect
26. C2×#14519700C22semidirect
35. C2×C4×#92418C22semidirect
38. #16839668C22semidirect
39. #16839660C22semidirect
42. #16839628C22semidirect
44. #16839524C22semidirect
45. #16839524C22semidirect
46. #16839524C22semidirect
47. #16839524C22semidirect
48. #16839517C22semidirect
49. #16839517C22semidirect
447. C61#24905semidirect

Maximal subgroups

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

subgroupindex
C2×#168399132
C2×C4×#117582002
#214493222
#214473402
#214472562
#214471362
#214470222
#214465052
#214464272
#214461772
#214461532
#214460662
#214458292
#214457502
D4×C22⋊C4×C612
#2490561