Finite Group Databasebeta

← #29686259

Subgroups — #29686259

Order 15616.

1260 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839955C211yesmaximal, characteristic
2C2×#16839872C211yesmaximal, characteristic, complemented
3C4×#14519773C211yesmaximal, characteristic, complemented
4C4×D4×Dic61C211yesmaximal, characteristic, complemented
5#21446744C211yesmaximal, characteristic, complemented
6#21446579C211yesmaximal, characteristic, complemented
7#21446449C211yesmaximal, characteristic, complemented
8#21446445C211yesmaximal, characteristic, complemented
9#21446169C211yesmaximal, characteristic, complemented
10#21446165C211yesmaximal, characteristic, complemented
11#21445817C211yesmaximal, characteristic, complemented
12#21445673C211yesmaximal, characteristic, complemented
13#21445645C211yesmaximal, characteristic, complemented
14#21445644C211yesmaximal, characteristic, complemented
15C2×C61×#442C211yesmaximal, characteristic, complemented
16C22×#11758199C2211yescharacteristic
17C2×#14519773C2211yescharacteristic
18C2×C4×D244C2211yescharacteristic
19C2×D4×Dic61C2211yescharacteristic
20C2×D4×Dic61C2211yescharacteristic
21C2×C4×C22⋊D61—21no—
22C2×C4×C22⋊D61—21no—
23C22×C4×Dic61—21no—
24#16839955C418yescomplemented
25#16839872—24no—
26C2×#14519708C2211yescharacteristic
27C2×#14519706C2211yescharacteristic
28C2×#14519706C2211yescharacteristic
29C2×#14519699C2211yescharacteristic
30C2×#14519699C2211yescharacteristic
31C2×#14519698C2211yescharacteristic
32C2×#14519698C2211yescharacteristic
33C2×#14519698C2211yescharacteristic
34C2×#14519697C2211yescharacteristic
35C2×#14519688C2211yescharacteristic
36#16839665C2211yescharacteristic
37#16839663C2211yescharacteristic
38#16839662—21no—
39#16839662—21no—
40#16839631C2211yescharacteristic
41C4⋊C4×Dic61C2211yescharacteristic
42C4⋊C4×Dic61C2211yescharacteristic
43C4×C4⋊Dic61C2211yescharacteristic
44C22⋊C4×Dic61—21no—
45C22⋊C4×Dic61—21no—
46C4×C22⋊Dic61—21no—
47C42×Dic61C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54C22×D8×C61C2211yescharacteristic
55C2×C4×D4×C61C2211yescharacteristic
56C2×C4×D4×C61C2211yescharacteristic
57C61×#442—24no—
58C2×#106×C61C2211yescharacteristic
59C2×#102×C61C2211yescharacteristic
60C2×#102×C61C2211yescharacteristic
61C2×#97×C61C2211yescharacteristic
62C22×D244C2311yescharacteristic
63C22×C22⋊D61—21no—
64C22×C22⋊D61—21no—
65C23×Dic61—21no—
66C23×Dic61—21no—
67C22×C4×D61—21no—
68C2×#11758199—22no—
69C2×#11758199—22no—
70C2×#11758199C2×C414yescomplemented
71C22×#92418C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73#14519773—22no—
74#14519773C2×C414yescomplemented
75C4×D244—22no—
76C4×D244—22no—
77D4×Dic61—22no—
78D4×Dic61—22no—
79D4×Dic61—22no—
80D4×Dic61C2×C414yescomplemented
81C4×C22⋊D61—44no—
82C4×C22⋊D61—44no—
83C2×C4⋊Dic61C2311yescharacteristic
84C2×C4⋊Dic61C2311yescharacteristic
85C2×C4⋊Dic61C2311yescharacteristic
86C2×#11758196—21no—
87C2×#11758196—21no—
88C2×C22⋊Dic61—21no—
89C2×C22⋊Dic61—21no—
90C2×C22⋊Dic61—21no—
91C2×C22⋊Dic61—21no—
92C2×#11758198—21no—
93C2×#11758198—21no—
94C2×#11758198—21no—
95C2×C4×Dic61—21no—
96C2×C4×Dic61—21no—
97C2×C4×Dic61—21no—
98C2×C4×Dic61—44no—
99C2×C4×Dic61D411yescharacteristic
100C2×C4×Dic61D411yescharacteristic
101C2×C4×Dic61D411yescharacteristic
102C2×C4×Dic61D411yescharacteristic
103C2×C4×Dic61C2311yescharacteristic
104C2×C4×Dic61C2311yescharacteristic
105#14519708—22no—
106#14519706—22no—
107#14519706C2×C414yescomplemented
108#14519699—22no—
109#14519699C2×C414yescomplemented
110#14519698—22no—
111#14519698—22no—
112#14519698C2×C414yescomplemented
113#14519697—22no—
114#14519688—22no—
115#14519684—21no—
116#14519684—21no—
117#14519684—21no—
118C22×D4×C61C2311yescharacteristic
119C22×D4×C61C2311yescharacteristic
120C23×C4×C61—21no—
121C23×C4×C61—21no—
122C2×D8×C61—22no—
123C2×D8×C61—22no—
124C2×D8×C61C2×C414yescomplemented
125C22×C8×C61C2311yescharacteristic
126C22×C8×C61C2311yescharacteristic
127C4×D4×C61—22no—
128C4×D4×C61—22no—
129C4×D4×C61—22no—
130C4×D4×C61D414yescomplemented
131C2×C4⋊C4×C61C2311yescharacteristic
132C2×C4⋊C4×C61C2311yescharacteristic
133C2×C22⋊C4×C61—21no—
134C2×C22⋊C4×C61—21no—
135C2×C42×C61C2311yescharacteristic
136#106×C61—22no—
137#102×C61—22no—
138#102×C61—22no—
139#97×C61—22no—
140C24×C61—21no—
141C24×C61—21no—
142C23×D61—21no—
143C2×D4×C61—21no—
144C2×D4×C61—21no—
145C2×D4×C61—21no—
146C2×D4×C61—21no—
147C2×D4×C61—21no—
148C2×D4×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61C22×C412yes—
152C2×D4×C61C22×C412yes—
153C2×D4×C61C2×D412yes—
154C2×D4×C61#4112yes—
155C22×C4×C61—21no—
156C22×C4×C61—24no—
157C22×C4×C61—21no—
158C22×C4×C61—42no—
159C22×C4×C61—42no—
160C22×C4×C61—42no—
161C22×C4×C61—42no—
162C22×C4×C61—42no—
163C22×C4×C61C2×D411yescharacteristic
164C22×C4×C61C2×D411yescharacteristic
165C22×C4×C61C2411yescharacteristic
166C2×C22⋊D61—24no—
167C2×C22⋊D61—24no—
168C2×C22⋊D61—42no—
169C2×C22⋊D61—42no—
170C2×C22⋊D61—42no—
171C2×C22⋊D61—42no—
172C22×Dic61—24no—
173C22×Dic61—21no—
174C22×Dic61—21no—
175C22×Dic61—24no—
176C22×Dic61—21no—
177C22×Dic61—42no—
178C22×Dic61—42no—
179C22×Dic61—42no—
180C22×Dic61—42no—
181C22×Dic61C2×D411yescharacteristic
182C22×Dic61C2×D411yescharacteristic
183C22×Dic61C2×D411yescharacteristic
184C22×Dic61C2×D411yescharacteristic
185C2×D244—21no—
186C2×D244—21no—
187C2×D244—21no—
188C2×D244—21no—
189C2×D244—21no—
190C2×D244C22×C412yes—
191C2×C4×D61—42no—
192C2×C4×D61—42no—
193C2×C4×D61—42no—
194D8×C61—28no—
195C2×C8×C61—21no—
196C2×C8×C61—21no—
197C2×C8×C61—21no—
198C2×C8×C61—21no—
199C2×C8×C61—21no—
200C2×C8×C61C22×C412yes—
201C4⋊C4×C61—21no—
202C4⋊C4×C61—21no—
203C4⋊C4×C61—21no—
204C4⋊C4×C61C2×D412yes—
205C22⋊C4×C61—24no—
206C22⋊C4×C61—42no—
207C42×C61C2×D412yes—
208C42×C61#4112yes—
209C22⋊Dic61—24no—
210C22⋊Dic61—24no—
211C22⋊Dic61—42no—
212C22⋊Dic61—42no—
213#11758199—28no—
214#11758198—42no—
215#11758198—42no—
216#11758198—42no—
217C4⋊Dic61—21no—
218C4⋊Dic61—21no—
219C4⋊Dic61—21no—
220C4⋊Dic61—21no—
221C4⋊Dic61C22×C412yes—
222C4⋊Dic61#4112yes—
223#11758196—42no—
224#11758196—42no—
225C4×Dic61—21no—
226C4×Dic61—21no—
227C4×Dic61—22no—
228C4×Dic61—22no—
229C4×Dic61—22no—
230C4×Dic61—41no—
231C4×Dic61—42no—
232C4×Dic61—42no—
233C4×Dic61—42no—
234C4×Dic61C22×C412yes—
235C4×Dic61#4112yes—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418C22×C412yes—
242C23×C61—22no—
243C23×C61—22no—
244C23×C61—22no—
245C23×C61—22no—
246C23×C61—41no—
247C23×C61—41no—
248C23×C61—41no—
249C23×C61—41no—
250C23×C61—41no—
251C23×C61—41no—
252C23×C61—41no—
253C23×C61—41no—
254C23×C61—41no—
255C23×C61—41no—
256C23×C61C22×D411yescharacteristic
257C22×D61—22no—
258C22×D61—41no—
259C22×D61—41no—
260C22×D61—41no—
261C22×D61—41no—
262C22×D61—41no—
263C22×D61—41no—
264D4×C61—22no—
265D4×C61—22no—
266D4×C61—22no—
267D4×C61—22no—
268D4×C61—22no—
269D4×C61—41no—
270D4×C61—41no—
271D4×C61C4×D414yescomplemented
272C2×C4×C61—21no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—21no—
276C2×C4×C61—22no—
277C2×C4×C61—48no—
278C2×C4×C61—41no—
279C2×C4×C61—41no—
280C2×C4×C61—41no—
281C2×C4×C61—41no—
282C2×C4×C61—41no—
283C2×C4×C61—84no—
284C2×C4×C61#12112yes—
285C2×C4×C61#12112yes—
286C2×C4×C61C23×C411yescharacteristic
287C2×C4×C61C22×D411yescharacteristic
288C2×C4×C61C2×#4111yescharacteristic
289C2×C4×C61C2×#4111yescharacteristic
290C2×C4×C61C2×#4111yescharacteristic
291C2×C4×C61C2×#4111yescharacteristic
292C22⋊D61—48no—
293C22⋊D61—48no—
294C2×Dic61—21no—
295C2×Dic61—21no—
296C2×Dic61—21no—
297C2×Dic61—21no—
298C2×Dic61—22no—
299C2×Dic61—21no—
300C2×Dic61—22no—
301C2×Dic61—21no—
302C2×Dic61—21no—
303C2×Dic61—48no—
304C2×Dic61—41no—
305C2×Dic61—41no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308C2×Dic61—48no—
309C2×Dic61—41no—
310C2×Dic61—41no—
311C2×Dic61—41no—
312C2×Dic61C4×D412yes—
313C2×Dic61C4×D412yes—
314C2×Dic61AGL(1,ℤ/8)12yes—
315C2×Dic61AGL(1,ℤ/8)12yes—
316C2×Dic61AGL(1,ℤ/8)12yes—
317D244—22no—
318D244—22no—
319D244—41no—
320D244—41no—
321C4×D61—84no—
322C8×C61—22no—
323C8×C61—41no—
324#92418—22no—
325#92418—41no—
326#21503—611nomaximal, Sylow
327C22×C61—24no—
328C22×C61—42no—
329C22×C61—42no—
330C22×C61—42no—
331C22×C61—42no—
332C22×C61—42no—
333C22×C61—42no—
334C22×C61—42no—
335C22×C61—42no—
336C22×C61—42no—
337C22×C61—81no—
338C22×C61—81no—
339C22×C61—81no—
340C22×C61—81no—
341C22×C61C2×C4×D411yescharacteristic
342C22×C61C2×#12111yescharacteristic
343C22×C61#52511yescharacteristic
344C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
345C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
346C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
347C22×C61#57511yescharacteristic
348C2×D61—42no—
349C2×D61—42no—
350C2×D61—42no—
351C2×D61—81no—
352C2×D61—81no—
353C2×D61—81no—
354C2×D61—81no—
355C4×C61—22no—
356C4×C61—22no—
357C4×C61—42no—
358C4×C61—81no—
359C4×C61C2×C4×D411yescharacteristic
360C4×C61C4×#4111yescharacteristic
361C4×C61#52911yescharacteristic
362C4×C61#53211yescharacteristic
363Dic61—22no—
364Dic61—22no—
365Dic61—42no—
366Dic61—41no—
367Dic61—42no—
368Dic61—81no—
369Dic61#44214yescomplemented
370C2×#459—611no—
371C2×#442—611no—
372C2×#442D6111yescharacteristic, complemented
373C4×#127—611no—
374C42×D4—611no—
375#1982—611no—
376#1948—611no—
377#1926—611no—
378#1926—611no—
379#1879—611no—
380#1879—611no—
381#1802—611no—
382#1767—611no—
383#1762—611no—
384#1762—611no—
385C2×C61—44no—
386C2×C61—82no—
387C2×C61C4×#12111yescharacteristic
388C2×C61C2×#44211yescharacteristic
389C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
390C2×C61#303611yescharacteristic
391C2×C61#303811yescharacteristic
392C2×C61#310911yescharacteristic
393C2×C61#311511yescharacteristic
394D61—82no—
395C22×D8—611no—
396C22×D8C2×D6111yescharacteristic
397C2×#127—611no—
398C2×C4×D4—611no—
399C2×C4×D4—611no—
400C2×C4×D4—611no—
401C2×C4×D4—1221no—
402C2×C4×D4—1221no—
403C2×C4×D4C2×D6111yescharacteristic
404C2×C4×D4C2×D6111yescharacteristic
405C22×C42—1221no—
406#459—618no—
407#442—24no—
408#442—1224no—
409C2×#106—611no—
410C2×#106C2×D6111yescharacteristic
411C2×C4⋊C8—611no—
412C2×C4⋊C8—611no—
413C2×#102—611no—
414C2×#102—611no—
415C2×#102—611no—
416C2×#102—611no—
417C2×#102—611no—
418C2×#102—611no—
419C2×#102C2×D6111yescharacteristic
420C2×#102C2×D6111yescharacteristic
421C2×#97—611no—
422C2×#97C2×D6111yescharacteristic
423#390—611no—
424#390—611no—
425#390—1221no—
426#390—1221no—
427#384—611no—
428C4×C4⋊C4—611no—
429C4×C4⋊C4—611no—
430C4×C4⋊C4—611no—
431C4×C22⋊C4—1221no—
432C4×C22⋊C4—1221no—
433C4×C22⋊C4—1221no—
434C43—611no—
435#340—611no—
436#340—611no—
437#340—611no—
438#340—611no—
439#336—611no—
440#336—611no—
441C61#2150311yescharacteristic, complemented, Sylow
442C22×D4—611no—
443C22×D4—1221no—
444C22×D4—1221no—
445C22×D4C22×D6111yescharacteristic
446C22×D4C22×D6111yescharacteristic
447C23×C4—21no—
448C23×C4—21no—
449C23×C4—1221no—
450C23×C4—1221no—
451C23×C4—1221no—
452C2×D8—22no—
453C2×D8—22no—
454C2×D8—614no—
455C2×D8—1222no—
456C2×D8—1222no—
457C2×D8C4×D6114yescomplemented
458C22×C8—611no—
459C22×C8—611no—
460C22×C8C22×D6111yescharacteristic
461C22×C8C22×D6111yescharacteristic
462#127—614no—
463#127—1222no—
464C4×D4—22no—
465C4×D4—22no—
466C4×D4—22no—
467C4×D4—614no—
468C4×D4—1222no—
469C4×D4—1222no—
470C4×D4—1222no—
471C4×D4—1222no—
472C4×D4—1222no—
473C4×D4—2444no—
474C4×D4—2444no—
475C4×D4C22⋊D6114yescomplemented
476C2×C4⋊C4—611no—
477C2×C4⋊C4—611no—
478C2×C4⋊C4—611no—
479C2×C4⋊C4—1221no—
480C2×C4⋊C4—1221no—
481C2×C4⋊C4C22×D6111yescharacteristic
482C2×C4⋊C4C22×D6111yescharacteristic
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—1221no—
486C2×C22⋊C4—1221no—
487C2×C22⋊C4—1221no—
488C2×C22⋊C4—1221no—
489C2×C22⋊C4—1221no—
490C2×C22⋊C4—1221no—
491C2×C22⋊C4—1221no—
492C2×C42—611no—
493C2×C42—611no—
494C2×C42—611no—
495C2×C42—611no—
496C2×C42—611no—
497C2×C42—611no—
498C2×C42—1221no—
499C2×C42—1221no—
500C2×C42—1221no—
501C2×C42—2444no—
502C2×C42C22×D6111yescharacteristic
503#106—22no—
504#106—1222no—
505C4⋊C8—614no—
506C4⋊C8—1222no—
507#102—22no—
508#102—22no—
509#102—614no—
510#102—614no—
511#102—1222no—
512#102—1222no—
513#102—1222no—
514#102—1222no—
515#97—22no—
516#97—1222no—
517#95—1221no—
518#95—1221no—
519#95—1221no—
520C24—21no—
521C24—21no—
522C24—1221no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—612no—
532C2×D4—1224no—
533C2×D4—1224no—
534C2×D4—1221no—
535C2×D4—1221no—
536C2×D4—1221no—
537C2×D4—1221no—
538C2×D4—1221no—
539C2×D4—2442no—
540C2×D4—2442no—
541C2×D4—2442no—
542C2×D4—2442no—
543C2×D4C2×C4×D6112yes—
544C2×D4C2×C4×D6112yes—
545C2×D4#1175822212yes—
546C2×D4C2×C22⋊D6112yes—
547C22×C4—21no—
548C22×C4—24no—
549C22×C4—21no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—611no—
556C22×C4—611no—
557C22×C4—611no—
558C22×C4—611no—
559C22×C4—1224no—
560C22×C4—1224no—
561C22×C4—1221no—
562C22×C4—1221no—
563C22×C4—1221no—
564C22×C4—2442no—
565C22×C4—2442no—
566C22×C4—2442no—
567C22×C4—2442no—
568C22×C4—2442no—
569C22×C4—2442no—
570C22×C4—2442no—
571C22×C4D4×D6111yescharacteristic
572C22×C4D4×D6111yescharacteristic
573C22×C4C23×D6111yescharacteristic
574D8—28no—
575D8—1228no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—612no—
582C2×C8—1221no—
583C2×C8—1221no—
584C2×C8—1221no—
585C2×C8—1221no—
586C2×C8—1221no—
587C2×C8C2×C4×D6112yes—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—612no—
592C4⋊C4—612no—
593C4⋊C4—1221no—
594C4⋊C4—1221no—
595C4⋊C4—1221no—
596C4⋊C4—1221no—
597C4⋊C4—2442no—
598C4⋊C4—2442no—
599C4⋊C4C2×C22⋊D6112yes—
600C22⋊C4—24no—
601C22⋊C4—42no—
602C22⋊C4—1224no—
603C22⋊C4—1224no—
604C22⋊C4—2442no—
605C22⋊C4—2442no—
606C22⋊C4—2442no—
607C22⋊C4—2442no—
608C22⋊C4—2442no—
609C42—612no—
610C42—612no—
611C42—1222no—
612C42—1222no—
613C42—1222no—
614C42—1221no—
615C42—1221no—
616C42—2441no—
617C42—2442no—
618C42—2442no—
619C42—2442no—
620C42#1175822412yes—
621C42C2×C22⋊D6112yes—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—1222no—
637C23—2441no—
638C23—2441no—
639C23—2441no—
640C23—2441no—
641C23—2441no—
642C23—2441no—
643C23C2×D4×D6111yescharacteristic
644D4—22no—
645D4—22no—
646D4—22no—
647D4—22no—
648D4—22no—
649D4—41no—
650D4—41no—
651D4—1222no—
652D4—1222no—
653D4—2448no—
654D4—2448no—
655D4—2441no—
656D4—2441no—
657D4C4×C22⋊D6114yescomplemented
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—22no—
663C2×C4—48no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—84no—
670C2×C4—612no—
671C2×C4—612no—
672C2×C4—612no—
673C2×C4—612no—
674C2×C4—612no—
675C2×C4—1221no—
676C2×C4—1221no—
677C2×C4—1221no—
678C2×C4—1221no—
679C2×C4—1222no—
680C2×C4—1221no—
681C2×C4—1222no—
682C2×C4—1221no—
683C2×C4—1221no—
684C2×C4—4884no—
685C2×C4—2448no—
686C2×C4—2448no—
687C2×C4—2441no—
688C2×C4—2441no—
689C2×C4—2441no—
690C2×C4—2441no—
691C2×C4—2441no—
692C2×C4—2441no—
693C2×C4—2441no—
694C2×C4#1451974912yes—
695C2×C4#1451974912yes—
696C2×C4C22×C4×D6111yescharacteristic
697C2×C4C22×C22⋊D6111yescharacteristic
698C2×C4#41×D6111yescharacteristic
699C2×C4#41×D6111yescharacteristic
700C2×C4C2×#1175822411yescharacteristic
701C2×C4C2×#1175822211yescharacteristic
702C8—22no—
703C8—41no—
704C8—1222no—
705C8—2441no—
706C22—24no—
707C22—42no—
708C22—42no—
709C22—42no—
710C22—42no—
711C22—42no—
712C22—42no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—81no—
717C22—81no—
718C22—81no—
719C22—81no—
720C22—4881no—
721C22—4881no—
722C22—4881no—
723C22—4881no—
724C22—2442no—
725C22—2442no—
726C22—2442no—
727C22C4×D4×D6111yescharacteristic
728C22C2×#1451974911yescharacteristic
729C22#1684027111yescharacteristic
730C22AGL(1,ℤ/8)×D6111yescharacteristic
731C22AGL(1,ℤ/8)×D6111yescharacteristic
732C22AGL(1,ℤ/8)×D6111yescharacteristic
733C22#1684055811yescharacteristic
734C4—22no—
735C4—22no—
736C4—42no—
737C4—81no—
738C4—614no—
739C4—1222no—
740C4—1222no—
741C4—4881no—
742C4—2442no—
743C4—2442no—
744C4—2441no—
745C4C2×C4×C22⋊D6111yescharacteristic
746C4C4×#1175822411yescharacteristic
747C4#1684029211yescharacteristic
748C4#1684030811yescharacteristic
749C2—44no—
750C2—82no—
751C2—4882no—
752C2C4×#1451974911yescharacteristic
753C2#442×D6111yescharacteristic
754C2#2145463011yescharacteristic
755C2#2145528011yescharacteristic
756C2#2145529711yescharacteristic
757C2#2145590811yescharacteristic
758C2#2145596611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#442C2
socleC23×C61C22×D4
prime radicalC2×#16839955C2
cosocleC22×C4×C61C24
hypercenterC2×#442D61
hypocenterC61#21503
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
2. C2×#16839872C2semidirect
3. C4×#14519773C2semidirect
4. C4×D4×Dic61C2semidirect
5. #21446744C2semidirect
6. #21446579C2semidirect
7. #21446449C2semidirect
8. #21446445C2semidirect
9. #21446169C2semidirect
10. #21446165C2semidirect
11. #21445817C2semidirect
12. #21445673C2semidirect
13. #21445645C2semidirect
14. #21445644C2semidirect
15. C2×C61×#442C2semidirect
24. #16839955C4semidirect
70. C2×#11758199C2×C4semidirect
74. #14519773C2×C4semidirect
80. D4×Dic61C2×C4semidirect
107. #14519706C2×C4semidirect
109. #14519699C2×C4semidirect
112. #14519698C2×C4semidirect
124. C2×D8×C61C2×C4semidirect
130. C4×D4×C61D4semidirect
271. D4×C61C4×D4semidirect
369. Dic61#442semidirect
372. C2×#442D61semidirect
441. C61#21503semidirect
457. C2×D8C4×D61semidirect
475. C4×D4C22⋊D61semidirect
657. D4C4×C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168399552
C2×#168398722
C4×#145197732
C4×D4×Dic612
#214467442
#214465792
#214464492
#214464452
#214461692
#214461652
#214458172
#214456732
#214456452
#214456442
C2×C61×#4422
#2150361