Finite Group Databasebeta

← #29686261

Subgroups — #29686261

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×#16839956C211yesmaximal, characteristic
2C2×#16839875C211yesmaximal, characteristic, complemented
3C2×#16839872C211yesmaximal, characteristic, complemented
4C4×#14519773C211yesmaximal, characteristic, complemented
5C4×#14519739C211yesmaximal, characteristic, complemented
6#21446744C211yesmaximal, characteristic, complemented
7#21446581C211yesmaximal, characteristic, complemented
8#21446448C211yesmaximal, characteristic, complemented
9#21446444C211yesmaximal, characteristic, complemented
10#21446168C211yesmaximal, characteristic, complemented
11#21446164C211yesmaximal, characteristic, complemented
12#21445818C211yesmaximal, characteristic, complemented
13#21445673C211yesmaximal, characteristic, complemented
14#21445647C211yesmaximal, characteristic, complemented
15C61×#1762C211yesmaximal, characteristic, complemented
16C22×D488C2211yescharacteristic
17C22×#11758199C2211yescharacteristic
18C2×#14519773C2211yescharacteristic
19C2×C4×D244C2211yescharacteristic
20C2×C4×D244C2211yescharacteristic
21C2×#14519739C2211yescharacteristic
22C2×#14519739C2211yescharacteristic
23C2×C4×C22⋊D61—21no—
24C2×C4×C22⋊D61—21no—
25C2×C42×D61—21no—
26#16839956C418yescomplemented
27#16839875—24no—
28#16839872—24no—
29C2×#14519709C2211yescharacteristic
30C2×#14519708C2211yescharacteristic
31C2×#14519706C2211yescharacteristic
32C2×#14519706C2211yescharacteristic
33C2×#14519699C2211yescharacteristic
34C2×#14519699C2211yescharacteristic
35C2×#14519698C2211yescharacteristic
36C2×#14519697C2211yescharacteristic
37C2×#14519697C2211yescharacteristic
38C2×#14519697C2211yescharacteristic
39C2×#14519688C2211yescharacteristic
40#16839665C2211yescharacteristic
41#16839663C2211yescharacteristic
42#16839662—21no—
43#16839662—21no—
44#16839631C2211yescharacteristic
45C4⋊C4×Dic61C2211yescharacteristic
46C4⋊C4×Dic61C2211yescharacteristic
47C4×#11758198—21no—
48#16839609—21no—
49#16839609—21no—
50C42×Dic61C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839516C2211yescharacteristic
54#16839516C2211yescharacteristic
55C2×C4×D4×C61C2211yescharacteristic
56C2×#102×C61C2211yescharacteristic
57C2×#102×C61C2211yescharacteristic
58C2×#97×C61C2211yescharacteristic
59C4×C4⋊C4×C61C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C61×#340C2211yescharacteristic
62C22×D244C2311yescharacteristic
63C22×D244C2311yescharacteristic
64C22×C22⋊D61—21no—
65C22×C22⋊D61—21no—
66C22×C4×D61—21no—
67C22×C4×D61—21no—
68C22×C4×D61—21no—
69C22×C4×D61—21no—
70C2×D488—22no—
71C2×D488—22no—
72C2×D488C2×C414yescomplemented
73C2×#11758199—22no—
74C2×#11758199—22no—
75C2×#11758199C2×C414yescomplemented
76C22×#92418C2311yescharacteristic
77C22×#92418C2311yescharacteristic
78#14519773—22no—
79#14519773C2×C414yescomplemented
80C4×D244—22no—
81C4×D244—22no—
82C4×D244—22no—
83C4×D244D414yescomplemented
84#14519739—22no—
85#14519739—22no—
86#14519739—22no—
87#14519739C2×C414yescomplemented
88C4×C22⋊D61—44no—
89C4×C22⋊D61—44no—
90C2×C4⋊Dic61C2311yescharacteristic
91C2×C4⋊Dic61C2311yescharacteristic
92C2×#11758196—21no—
93C2×#11758196—21no—
94C2×C22⋊Dic61—21no—
95C2×C22⋊Dic61—21no—
96C2×#11758198—21no—
97C2×#11758198—21no—
98C2×#11758198—21no—
99C2×#11758198—21no—
100C2×#11758198—21no—
101C2×#11758198—21no—
102C2×C4×Dic61—21no—
103C2×C4×Dic61—21no—
104C2×C4×Dic61D411yescharacteristic
105C2×C4×Dic61D411yescharacteristic
106C2×C4×Dic61D411yescharacteristic
107C2×C4×Dic61D411yescharacteristic
108C2×C4×Dic61C2311yescharacteristic
109C2×C4×Dic61C2311yescharacteristic
110C42×D61—44no—
111#14519709—22no—
112#14519708—22no—
113#14519706—22no—
114#14519706C2×C414yescomplemented
115#14519699—22no—
116#14519699—22no—
117#14519698—22no—
118#14519697—22no—
119#14519697—22no—
120#14519697C2×C414yescomplemented
121#14519688—22no—
122#14519684—21no—
123#14519684—21no—
124C22×D4×C61C2311yescharacteristic
125C23×C4×C61—21no—
126C22×C8×C61C2311yescharacteristic
127C22×C8×C61C2311yescharacteristic
128C4×D4×C61—22no—
129C4×D4×C61—22no—
130C2×C4⋊C4×C61C2311yescharacteristic
131C2×C4⋊C4×C61C2311yescharacteristic
132C2×C4⋊C4×C61C2311yescharacteristic
133C2×C22⋊C4×C61—21no—
134C2×C42×C61—21no—
135C2×C42×C61C2311yescharacteristic
136#102×C61—22no—
137#102×C61C2×C414yescomplemented
138#97×C61—22no—
139#95×C61—21no—
140C24×C61—21no—
141C23×D61—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×C61C22×C412yes—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—42no—
153C22×C4×C61—42no—
154C22×C4×C61—42no—
155C22×C4×C61C2×D411yescharacteristic
156C22×C4×C61C2×D411yescharacteristic
157C22×C4×C61C2411yescharacteristic
158C2×C22⋊D61—24no—
159C2×C22⋊D61—24no—
160C2×C22⋊D61—42no—
161C2×C22⋊D61—42no—
162C2×C22⋊D61—42no—
163C2×C22⋊D61—42no—
164C22×Dic61—21no—
165C22×Dic61—21no—
166C22×Dic61C2×D411yescharacteristic
167C22×Dic61C2×D411yescharacteristic
168C22×Dic61C2×D411yescharacteristic
169C22×Dic61C2×D411yescharacteristic
170C2×D244—21no—
171C2×D244—21no—
172C2×D244—21no—
173C2×D244—21no—
174C2×D244—21no—
175C2×D244—21no—
176C2×D244—21no—
177C2×D244—21no—
178C2×D244C22×C412yes—
179C2×D244C22×C412yes—
180C2×D244C2×D412yes—
181C2×D244#4112yes—
182C2×C4×D61—24no—
183C2×C4×D61—24no—
184C2×C4×D61—24no—
185C2×C4×D61—42no—
186C2×C4×D61—42no—
187C2×C4×D61—42no—
188C2×C4×D61—42no—
189C2×C4×D61—42no—
190C2×C4×D61—42no—
191C2×C4×D61—42no—
192C2×C4×D61—42no—
193C2×C4×D61—42no—
194C2×C8×C61—21no—
195C2×C8×C61—21no—
196C2×C8×C61—21no—
197C2×C8×C61—21no—
198C2×C8×C61—21no—
199C2×C8×C61C22×C412yes—
200C4⋊C4×C61—21no—
201C4⋊C4×C61—21no—
202C4⋊C4×C61—21no—
203C4⋊C4×C61—21no—
204C4⋊C4×C61C22×C412yes—
205C4⋊C4×C61#4112yes—
206C22⋊C4×C61—42no—
207C42×C61—42no—
208C42×C61C2×D412yes—
209C42×C61#4112yes—
210C22⋊Dic61—42no—
211C22⋊Dic61—42no—
212#11758199—28no—
213#11758198—24no—
214#11758198—24no—
215#11758198—24no—
216#11758198—42no—
217#11758198—42no—
218#11758198—42no—
219C4⋊Dic61—21no—
220C4⋊Dic61—21no—
221C4⋊Dic61—21no—
222C4⋊Dic61C2×D412yes—
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×Dic61C22×C412yes—
234C4×Dic61#4112yes—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418C22×C412yes—
241D488—28no—
242C23×C61—22no—
243C23×C61—41no—
244C23×C61—41no—
245C23×C61—41no—
246C23×C61—41no—
247C23×C61—41no—
248C23×C61—41no—
249C23×C61C22×D411yescharacteristic
250C22×D61—22no—
251C22×D61—22no—
252C22×D61—22no—
253C22×D61—22no—
254C22×D61—41no—
255C22×D61—41no—
256C22×D61—41no—
257C22×D61—41no—
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—41no—
267D4×C61—41no—
268C2×C4×C61—21no—
269C2×C4×C61—21no—
270C2×C4×C61—21no—
271C2×C4×C61—21no—
272C2×C4×C61—22no—
273C2×C4×C61—22no—
274C2×C4×C61—41no—
275C2×C4×C61—41no—
276C2×C4×C61—41no—
277C2×C4×C61—41no—
278C2×C4×C61—41no—
279C2×C4×C61—41no—
280C2×C4×C61—41no—
281C2×C4×C61—84no—
282C2×C4×C61#12112yes—
283C2×C4×C61#12112yes—
284C2×C4×C61C23×C411yescharacteristic
285C2×C4×C61C22×D411yescharacteristic
286C2×C4×C61C2×#4111yescharacteristic
287C2×C4×C61C2×#4111yescharacteristic
288C2×C4×C61C2×#4111yescharacteristic
289C2×C4×C61C2×#4111yescharacteristic
290C22⋊D61—48no—
291C22⋊D61—48no—
292C2×Dic61—21no—
293C2×Dic61—21no—
294C2×Dic61—21no—
295C2×Dic61—21no—
296C2×Dic61—22no—
297C2×Dic61—21no—
298C2×Dic61—21no—
299C2×Dic61—21no—
300C2×Dic61—41no—
301C2×Dic61—41no—
302C2×Dic61—41no—
303C2×Dic61—41no—
304C2×Dic61—41no—
305C2×Dic61C4×D412yes—
306C2×Dic61C4×D412yes—
307C2×Dic61AGL(1,ℤ/8)12yes—
308C2×Dic61AGL(1,ℤ/8)12yes—
309C2×Dic61AGL(1,ℤ/8)12yes—
310D244—22no—
311D244—22no—
312D244—22no—
313D244—22no—
314D244—22no—
315D244—41no—
316D244—41no—
317D244C4×D414yescomplemented
318C4×D61—48no—
319C4×D61—48no—
320C4×D61—48no—
321C4×D61—84no—
322C8×C61—22no—
323C8×C61—41no—
324#92418—22no—
325#92418—41no—
326#21503—611nomaximal, Sylow
327C22×C61—42no—
328C22×C61—42no—
329C22×C61—42no—
330C22×C61—81no—
331C22×C61—81no—
332C22×C61—81no—
333C22×C61—81no—
334C22×C61C2×C4×D411yescharacteristic
335C22×C61C2×#12111yescharacteristic
336C22×C61#52511yescharacteristic
337C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
338C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
339C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
340C22×C61#57511yescharacteristic
341C2×D61—24no—
342C2×D61—42no—
343C2×D61—42no—
344C2×D61—42no—
345C2×D61—42no—
346C2×D61—42no—
347C2×D61—42no—
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—42no—
359C4×C61—81no—
360C4×C61C2×C4×D411yescharacteristic
361C4×C61C4×#4111yescharacteristic
362C4×C61#52911yescharacteristic
363C4×C61#53211yescharacteristic
364Dic61—22no—
365Dic61—22no—
366Dic61—41no—
367Dic61—42no—
368Dic61—81no—
369Dic61#44214yescomplemented
370C2×#459—611no—
371C2×#442—611no—
372C2×#442—611no—
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#1762D6111yescharacteristic, complemented
385C2×C61—82no—
386C2×C61C4×#12111yescharacteristic
387C2×C61C2×#44211yescharacteristic
388C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
389C2×C61#303611yescharacteristic
390C2×C61#303811yescharacteristic
391C2×C61#310911yescharacteristic
392C2×C61#311511yescharacteristic
393D61—44no—
394D61—82no—
395C22×D8—611no—
396C22×D8—611no—
397C2×#127—611no—
398C2×C4×D4—611no—
399C2×C4×D4—611no—
400C2×C4×D4—611no—
401C2×C4×D4—611no—
402C2×C4×D4—1221no—
403C2×C4×D4—1221no—
404C2×C4×D4C2×D6111yescharacteristic
405C22×C42—1221no—
406#459—618no—
407#442—1224no—
408#442—1224no—
409C2×#106—611no—
410C2×#106—611no—
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⋊C4C2×D6111yescharacteristic
431C4×C22⋊C4—1221no—
432C4×C22⋊C4—1221no—
433C4×C22⋊C4—1221no—
434C43—611no—
435#340—611no—
436#340—611no—
437#340C2×D6111yescharacteristic
438#340C2×D6111yescharacteristic
439#336—611no—
440#336—611no—
441C61#2150311yescharacteristic, complemented, Sylow
442C22×D4—611no—
443C22×D4—611no—
444C22×D4—1221no—
445C22×D4—1221no—
446C22×D4C22×D6111yescharacteristic
447C23×C4—21no—
448C23×C4—1221no—
449C23×C4—1221no—
450C23×C4—1221no—
451C23×C4—1221no—
452C2×D8—614no—
453C2×D8—614no—
454C2×D8—1222no—
455C2×D8—1222no—
456C2×D8—1222no—
457C2×D8—1222no—
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—614no—
467C4×D4—614no—
468C4×D4—1222no—
469C4×D4—1222no—
470C4×D4—1222no—
471C4×D4—1222no—
472C4×D4—1222no—
473C4×D4—1222no—
474C4×D4—2444no—
475C4×D4—2444no—
476C2×C4⋊C4—611no—
477C2×C4⋊C4—611no—
478C2×C4⋊C4—1221no—
479C2×C4⋊C4—1221no—
480C2×C4⋊C4C22×D6111yescharacteristic
481C2×C4⋊C4C22×D6111yescharacteristic
482C2×C4⋊C4C22×D6111yescharacteristic
483C2×C22⋊C4—21no—
484C2×C22⋊C4—1221no—
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—21no—
493C2×C42—611no—
494C2×C42—611no—
495C2×C42—611no—
496C2×C42—611no—
497C2×C42—611no—
498C2×C42—611no—
499C2×C42—1221no—
500C2×C42—1221no—
501C2×C42—2444no—
502C2×C42C22×D6111yescharacteristic
503#106—1222no—
504#106—1222no—
505C4⋊C8—614no—
506C4⋊C8—1222no—
507#102—22no—
508#102—614no—
509#102—1222no—
510#102—1222no—
511#102—1222no—
512#102—1222no—
513#102—1222no—
514#102C4×D6114yescomplemented
515#97—22no—
516#97—1222no—
517#95—21no—
518#95—1221no—
519#95—1221no—
520C24—21no—
521C24—1221no—
522C24—1221no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—612no—
529C2×D4—612no—
530C2×D4—612no—
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—1221no—
540C2×D4—1221no—
541C2×D4—1221no—
542C2×D4—2442no—
543C2×D4—2442no—
544C2×D4—2442no—
545C2×D4—2442no—
546C2×D4C2×C4×D6112yes—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—611no—
554C22×C4—611no—
555C22×C4—611no—
556C22×C4—611no—
557C22×C4—1224no—
558C22×C4—1224no—
559C22×C4—1221no—
560C22×C4—1224no—
561C22×C4—1221no—
562C22×C4—2442no—
563C22×C4—2442no—
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—1228no—
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—21no—
592C4⋊C4—612no—
593C4⋊C4—1221no—
594C4⋊C4—1221no—
595C4⋊C4—1221no—
596C4⋊C4—2442no—
597C4⋊C4—2442no—
598C4⋊C4C2×C4×D6112yes—
599C4⋊C4#1175822212yes—
600C22⋊C4—42no—
601C22⋊C4—1224no—
602C22⋊C4—1224no—
603C22⋊C4—1224no—
604C22⋊C4—2442no—
605C22⋊C4—2442no—
606C22⋊C4—2442no—
607C22⋊C4—2442no—
608C22⋊C4—2442no—
609C42—42no—
610C42—612no—
611C42—612no—
612C42—1222no—
613C42—1222no—
614C42—1222no—
615C42—1221no—
616C42—1221no—
617C42—2441no—
618C42—2442no—
619C42—2442no—
620C42#1175822212yes—
621C42D4×D6112yes—
622C23—22no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—1222no—
630C23—1222no—
631C23—1222no—
632C23—1222no—
633C23—2441no—
634C23—2441no—
635C23—2441no—
636C23—2441no—
637C23—2441no—
638C23—2441no—
639C23—2441no—
640C23—2441no—
641C23—2441no—
642C23—2441no—
643C23C2×D4×D6111yescharacteristic
644D4—22no—
645D4—22no—
646D4—41no—
647D4—41no—
648D4—614no—
649D4—1222no—
650D4—1222no—
651D4—1222no—
652D4—1222no—
653D4—1222no—
654D4—2448no—
655D4—2448no—
656D4—2441no—
657D4—2441no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—84no—
672C2×C4—612no—
673C2×C4—612no—
674C2×C4—612no—
675C2×C4—612no—
676C2×C4—612no—
677C2×C4—1221no—
678C2×C4—1221no—
679C2×C4—1221no—
680C2×C4—1221no—
681C2×C4—1222no—
682C2×C4—1221no—
683C2×C4—1221no—
684C2×C4—1221no—
685C2×C4—4884no—
686C2×C4—2448no—
687C2×C4—2448no—
688C2×C4—2448no—
689C2×C4—2441no—
690C2×C4—2441no—
691C2×C4—2441no—
692C2×C4—2441no—
693C2×C4—2441no—
694C2×C4#1451975012yes—
695C2×C4#1451975012yes—
696C2×C4C22×C4×D6111yescharacteristic
697C2×C4C2×D4×D6111yescharacteristic
698C2×C4#41×D6111yescharacteristic
699C2×C4#41×D6111yescharacteristic
700C2×C4C2×#1175822211yescharacteristic
701C2×C4C2×#1175822211yescharacteristic
702C8—22no—
703C8—41no—
704C8—1222no—
705C8—2441no—
706C22—42no—
707C22—42no—
708C22—42no—
709C22—81no—
710C22—81no—
711C22—81no—
712C22—81no—
713C22—1224no—
714C22—4881no—
715C22—4881no—
716C22—4881no—
717C22—4881no—
718C22—2442no—
719C22—2442no—
720C22—2442no—
721C22—2442no—
722C22—2442no—
723C22—2442no—
724C22—2442no—
725C22—2442no—
726C22—2442no—
727C22C4×D4×D6111yescharacteristic
728C22C2×#1451975011yescharacteristic
729C22#1684027111yescharacteristic
730C22AGL(1,ℤ/8)×D6111yescharacteristic
731C22AGL(1,ℤ/8)×D6111yescharacteristic
732C22AGL(1,ℤ/8)×D6111yescharacteristic
733C22#1684056111yescharacteristic
734C4—22no—
735C4—22no—
736C4—42no—
737C4—42no—
738C4—81no—
739C4—614no—
740C4—1222no—
741C4—1222no—
742C4—4881no—
743C4—2441no—
744C4—2442no—
745C4C4×D4×D6111yescharacteristic
746C4C4×#1175822211yescharacteristic
747C4#1684029011yescharacteristic
748C4#1684030911yescharacteristic
749C2—82no—
750C2—4882no—
751C2—2444no—
752C2C4×#1451975011yescharacteristic
753C2#442×D6111yescharacteristic
754C2#2145462411yescharacteristic
755C2#2145528211yescharacteristic
756C2#2145529811yescharacteristic
757C2#2145590811yescharacteristic
758C2#2145596811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1762C2
socleC23×C61C22×D4
prime radicalC2×#16839956C2
cosocleC22×C4×C61C24
hypercenter#1762D61
hypocenterC61#21503
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1762

Complements

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

NH ≅ G/Ntype
2. C2×#16839875C2semidirect
3. C2×#16839872C2semidirect
4. C4×#14519773C2semidirect
5. C4×#14519739C2semidirect
6. #21446744C2semidirect
7. #21446581C2semidirect
8. #21446448C2semidirect
9. #21446444C2semidirect
10. #21446168C2semidirect
11. #21446164C2semidirect
12. #21445818C2semidirect
13. #21445673C2semidirect
14. #21445647C2semidirect
15. C61×#1762C2semidirect
26. #16839956C4semidirect
72. C2×D488C2×C4semidirect
75. C2×#11758199C2×C4semidirect
79. #14519773C2×C4semidirect
83. C4×D244D4semidirect
87. #14519739C2×C4semidirect
114. #14519706C2×C4semidirect
120. #14519697C2×C4semidirect
137. #102×C61C2×C4semidirect
317. D244C4×D4semidirect
369. Dic61#442semidirect
384. #1762D61semidirect
441. C61#21503semidirect
514. #102C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168399562
C2×#168398752
C2×#168398722
C4×#145197732
C4×#145197392
#214467442
#214465812
#214464482
#214464442
#214461682
#214461642
#214458182
#214456732
#214456472
C61×#17622
#2150361