Finite Group Databasebeta

← #29686186

Subgroups — #29686186

Order 15616.

1272 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×D8×Dic61C211yesmaximal, characteristic, complemented
3C2×#16839842C211yesmaximal, characteristic, complemented
4#21448383C211yesmaximal, characteristic, complemented
5C4×D4×Dic61C211yesmaximal, characteristic, complemented
6#21446744C211yesmaximal, characteristic, complemented
7#21446576C211yesmaximal, characteristic, complemented
8#21446440C211yesmaximal, characteristic, complemented
9#21446436C211yesmaximal, characteristic, complemented
10#21446167C211yesmaximal, characteristic, complemented
11#21445817C211yesmaximal, characteristic, complemented
12#21445667C211yesmaximal, characteristic, complemented
13#102×Dic61C211yesmaximal, characteristic, complemented
14#21445633C211yesmaximal, characteristic, complemented
15C61×#1879C211yesmaximal, characteristic, complemented
16C22×#11758199C2211yescharacteristic
17C2×#14519773C2211yescharacteristic
18C2×D4×Dic61C2211yescharacteristic
19C2×D4×Dic61C2211yescharacteristic
20C2×D4×Dic61C2211yescharacteristic
21C2×#14519739C2211yescharacteristic
22C2×#14519737—21no—
23C2×#14519737—21no—
24C22×C4×Dic61—21no—
25#16839955C418yescomplemented
26D8×Dic61—24no—
27#16839842—24no—
28C2×#14519711C2211yescharacteristic
29C2×#14519710C2211yescharacteristic
30C2×#14519706C2211yescharacteristic
31C2×#14519706C2211yescharacteristic
32C2×#14519699C2211yescharacteristic
33C2×#14519699C2211yescharacteristic
34C2×#14519698C2211yescharacteristic
35C2×#14519698C2211yescharacteristic
36C2×#14519698C2211yescharacteristic
37C2×#14519697C2211yescharacteristic
38C2×C8×Dic61C2211yescharacteristic
39C2×C8×Dic61C2211yescharacteristic
40#16839664C2211yescharacteristic
41#16839662—21no—
42#16839662—21no—
43#16839631C2211yescharacteristic
44C4⋊C4×Dic61C2211yescharacteristic
45C4⋊C4×Dic61C2211yescharacteristic
46C4×C4⋊Dic61C2211yescharacteristic
47C22⋊C4×Dic61—21no—
48C22⋊C4×Dic61—21no—
49C4×C22⋊Dic61—21no—
50C42×Dic61C2211yescharacteristic
51#16839525C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839517C2211yescharacteristic
55C22×D8×C61C2211yescharacteristic
56C2×C4×D4×C61C2211yescharacteristic
57C2×#102×C61C2211yescharacteristic
58C2×#102×C61C2211yescharacteristic
59C61×#390C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C61×#336C2211yescharacteristic
62C22×D244C2311yescharacteristic
63C22×C22⋊D61—21no—
64C22×C22⋊D61—21no—
65C23×Dic61—21no—
66C23×Dic61—21no—
67C23×Dic61—21no—
68C22×C4×D61—21no—
69C2×#11758199—22no—
70C2×#11758199—22no—
71C2×#11758199C2×C414yescomplemented
72C22×#92418C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74#14519773—22no—
75#14519773C2×C414yescomplemented
76D4×Dic61—22no—
77D4×Dic61—22no—
78D4×Dic61—22no—
79D4×Dic61—22no—
80D4×Dic61C2×C414yescomplemented
81D4×Dic61D414yescomplemented
82#14519739—22no—
83#14519739—22no—
84#14519737—44no—
85#14519737—44no—
86C2×C4⋊Dic61C2311yescharacteristic
87C2×C4⋊Dic61C2311yescharacteristic
88C2×C4⋊Dic61C2311yescharacteristic
89C2×#11758196—21no—
90C2×#11758196—21no—
91C2×C22⋊Dic61—21no—
92C2×C22⋊Dic61—21no—
93C2×C22⋊Dic61—21no—
94C2×#11758198—21no—
95C2×#11758198—21no—
96C2×#11758198—21no—
97C2×C4×Dic61—21no—
98C2×C4×Dic61—21no—
99C2×C4×Dic61—21no—
100C2×C4×Dic61—44no—
101C2×C4×Dic61D411yescharacteristic
102C2×C4×Dic61D411yescharacteristic
103C2×C4×Dic61D411yescharacteristic
104C2×C4×Dic61D411yescharacteristic
105C2×C4×Dic61C2311yescharacteristic
106C2×C4×Dic61C2311yescharacteristic
107#14519711—22no—
108#14519710—22no—
109#14519706—22no—
110#14519706C2×C414yescomplemented
111#14519699—22no—
112#14519699C2×C414yescomplemented
113#14519698—22no—
114#14519698—22no—
115#14519698C2×C414yescomplemented
116#14519697—22no—
117C8×Dic61—22no—
118C8×Dic61—22no—
119#14519684—21no—
120#14519684—21no—
121#14519684—21no—
122C22×D4×C61C2311yescharacteristic
123C22×D4×C61C2311yescharacteristic
124C23×C4×C61—21no—
125C2×D8×C61—22no—
126C2×D8×C61—22no—
127C2×D8×C61C2×C414yescomplemented
128C22×C8×C61C2311yescharacteristic
129C22×C8×C61C2311yescharacteristic
130C4×D4×C61—22no—
131C4×D4×C61—22no—
132C2×C4⋊C4×C61C2311yescharacteristic
133C2×C4⋊C4×C61C2311yescharacteristic
134C2×C22⋊C4×C61—21no—
135C2×C22⋊C4×C61—21no—
136C2×C22⋊C4×C61—21no—
137C2×C42×C61C2311yescharacteristic
138#102×C61—22no—
139#102×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—24no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—42no—
159C22×C4×C61—42no—
160C22×C4×C61C2×D411yescharacteristic
161C22×C4×C61C2×D411yescharacteristic
162C22×C4×C61C2411yescharacteristic
163C2×C22⋊D61—24no—
164C2×C22⋊D61—24no—
165C2×C22⋊D61—42no—
166C2×C22⋊D61—42no—
167C2×C22⋊D61—42no—
168C2×C22⋊D61—42no—
169C22×Dic61—21no—
170C22×Dic61—21no—
171C22×Dic61—24no—
172C22×Dic61—24no—
173C22×Dic61—21no—
174C22×Dic61—42no—
175C22×Dic61—42no—
176C22×Dic61—42no—
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×C61#4112yes—
205C22⋊C4×C61—24no—
206C22⋊C4×C61—42no—
207C22⋊C4×C61—42no—
208C42×C61—21no—
209C42×C61—21no—
210C22⋊Dic61—24no—
211C22⋊Dic61—24no—
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⋊Dic61C2×D412yes—
223#11758196—42no—
224#11758196—42no—
225C4×Dic61—22no—
226C4×Dic61—22no—
227C4×Dic61—41no—
228C4×Dic61—42no—
229C4×Dic61—42no—
230C4×Dic61—42no—
231C4×Dic61D814yescomplemented
232C4×Dic61C22×C412yes—
233C4×Dic61C2×D412yes—
234C4×Dic61#4112yes—
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—22no—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61—48no—
279C2×C4×C61—41no—
280C2×C4×C61—41no—
281C2×C4×C61—41no—
282C2×C4×C61—41no—
283C2×C4×C61—41no—
284C2×C4×C61C2×D812yes—
285C2×C4×C61C23×C411yescharacteristic
286C2×C4×C61C22×D411yescharacteristic
287C2×C4×C61C2×#4111yescharacteristic
288C2×C4×C61C2×#4111yescharacteristic
289C2×C4×C61C2×#4111yescharacteristic
290C2×C4×C61C2×#4111yescharacteristic
291C22⋊D61—48no—
292C22⋊D61—48no—
293C2×Dic61—21no—
294C2×Dic61—21no—
295C2×Dic61—21no—
296C2×Dic61—21no—
297C2×Dic61—22no—
298C2×Dic61—22no—
299C2×Dic61—41no—
300C2×Dic61—41no—
301C2×Dic61—41no—
302C2×Dic61—41no—
303C2×Dic61—48no—
304C2×Dic61—48no—
305C2×Dic61—41no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308C2×Dic61—84no—
309C2×Dic61C4×D412yes—
310C2×Dic61C4×D412yes—
311C2×Dic61#12112yes—
312C2×Dic61#12112yes—
313C2×Dic61C2×D812yes—
314C2×Dic61C2×D812yes—
315C2×Dic61#13512yes—
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—
326C4×#459—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×C61C22×D811yescharacteristic
345C22×C61C2×#13511yescharacteristic
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—42no—
357C4×C61—41no—
358C4×C61—81no—
359C4×C61C2×C4×D411yescharacteristic
360C4×C61C4×#4111yescharacteristic
361C4×C61#52911yescharacteristic
362C4×C61#53211yescharacteristic
363Dic61—22no—
364Dic61—22no—
365Dic61—42no—
366Dic61—42no—
367Dic61—81no—
368Dic61C4×D814yescomplemented
369Dic61#45914yescomplemented
370C2×#459—611no—
371C2×C4×D8—611no—
372C2×C4×D8—611no—
373C4×#127—611no—
374C42×D4—611no—
375#1982—611no—
376#1947—611no—
377#1925—611no—
378#1925—611no—
379#1879—611no—
380#1879D6111yescharacteristic, complemented
381#1802—611no—
382C4×C4⋊C8—611no—
383C4×#102—611no—
384C4×#102—611no—
385C2×C61—44no—
386C2×C61—82no—
387C2×C61C4×#12111yescharacteristic
388C2×C61C2×C4×D811yescharacteristic
389C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
390C2×C61C2×#45911yescharacteristic
391C2×C61#303511yescharacteristic
392C2×C61#310011yescharacteristic
393C2×C61#310611yescharacteristic
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—611no—
402C2×C4×D4—1221no—
403C2×C4×D4—1221no—
404C2×C4×D4C2×D6111yescharacteristic
405C22×C42—1221no—
406#459—618no—
407C4×D8—1224no—
408C4×D8—1224no—
409C2×#107—611no—
410C2×#107—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×C4×C8—611no—
422C2×C4×C8—611no—
423#390—611no—
424#390—1221no—
425#390—1221no—
426#390C2×D6111yescharacteristic
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#340C2×D6111yescharacteristic
439#336—611no—
440#336C2×D6111yescharacteristic
441C61C4×#45911yescharacteristic, complemented, Sylow
442C22×D4—611no—
443C22×D4—1221no—
444C22×D4—1221no—
445C22×D4C22×D6111yescharacteristic
446C22×D4C22×D6111yescharacteristic
447C23×C4—21no—
448C23×C4—1221no—
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—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—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—21no—
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#107—1222no—
504#107—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—
515C4×C8—1222no—
516C4×C8—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×D4D4×D6112yes—
546C2×D4#1175822412yes—
547C22×C4—24no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—611no—
553C22×C4—611no—
554C22×C4—611no—
555C22×C4—611no—
556C22×C4—1224no—
557C22×C4—1224no—
558C22×C4—1221no—
559C22×C4—1221no—
560C22×C4—1221no—
561C22×C4—2442no—
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—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⋊C4#1175822412yes—
600C22⋊C4—24no—
601C22⋊C4—42no—
602C22⋊C4—42no—
603C22⋊C4—1224no—
604C22⋊C4—1224no—
605C22⋊C4—2442no—
606C22⋊C4—2442no—
607C22⋊C4—2442no—
608C22⋊C4—2442no—
609C42—21no—
610C42—21no—
611C42—612no—
612C42—612no—
613C42—612no—
614C42—612no—
615C42—614no—
616C42—1222no—
617C42—1222no—
618C42—2441no—
619C42—2442no—
620C42—2442no—
621C42—2442no—
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—
657D4#1451973714yescomplemented
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—48no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—612no—
671C2×C4—612no—
672C2×C4—612no—
673C2×C4—612no—
674C2×C4—612no—
675C2×C4—612no—
676C2×C4—612no—
677C2×C4—612no—
678C2×C4—1221no—
679C2×C4—1221no—
680C2×C4—1221no—
681C2×C4—1221no—
682C2×C4—1222no—
683C2×C4—1222no—
684C2×C4—4884no—
685C2×C4—4884no—
686C2×C4—2448no—
687C2×C4—2448no—
688C2×C4—2441no—
689C2×C4—2441no—
690C2×C4—2441no—
691C2×C4—2441no—
692C2×C4—2441no—
693C2×C4—2441no—
694C2×C4—2441no—
695C2×C4D8×D6112yes—
696C2×C4C22×C4×D6111yescharacteristic
697C2×C4C2×D4×D6111yescharacteristic
698C2×C4#41×D6111yescharacteristic
699C2×C4#41×D6111yescharacteristic
700C2×C4C2×#1175822411yescharacteristic
701C2×C4C2×#1175822411yescharacteristic
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
728C22#121×D6111yescharacteristic
729C22#1684026811yescharacteristic
730C22C2×D8×D6111yescharacteristic
731C22#135×D6111yescharacteristic
732C22AGL(1,ℤ/8)×D6111yescharacteristic
733C22#1684055811yescharacteristic
734C4—22no—
735C4—41no—
736C4—42no—
737C4—81no—
738C4—614no—
739C4—614no—
740C4—1222no—
741C4—1222no—
742C4—4881no—
743C4—2442no—
744C4—2442no—
745C4C2×#1451973711yescharacteristic
746C4C4×#1175822411yescharacteristic
747C4#1684028911yescharacteristic
748C4#1684030711yescharacteristic
749C2—44no—
750C2—82no—
751C2—4882no—
752C2#2144832911yescharacteristic
753C2C4×D8×D6111yescharacteristic
754C2#2145463011yescharacteristic
755C2#459×D6111yescharacteristic
756C2#2145527111yescharacteristic
757C2#2145581411yescharacteristic
758C2#2145587211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1879C2
socleC23×C61C22×D4
prime radicalC2×#16839955C2
cosocleC22×C4×C61C24
hypercenter#1879D61
hypocenterC61C4×#459
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1879

Complements

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

NH ≅ G/Ntype
2. C2×D8×Dic61C2semidirect
3. C2×#16839842C2semidirect
4. #21448383C2semidirect
5. C4×D4×Dic61C2semidirect
6. #21446744C2semidirect
7. #21446576C2semidirect
8. #21446440C2semidirect
9. #21446436C2semidirect
10. #21446167C2semidirect
11. #21445817C2semidirect
12. #21445667C2semidirect
13. #102×Dic61C2semidirect
14. #21445633C2semidirect
15. C61×#1879C2semidirect
25. #16839955C4semidirect
71. C2×#11758199C2×C4semidirect
75. #14519773C2×C4semidirect
80. D4×Dic61C2×C4semidirect
81. D4×Dic61D4semidirect
110. #14519706C2×C4semidirect
112. #14519699C2×C4semidirect
115. #14519698C2×C4semidirect
127. C2×D8×C61C2×C4semidirect
231. C4×Dic61D8semidirect
271. D4×C61C4×D4semidirect
368. Dic61C4×D8semidirect
369. Dic61#459semidirect
380. #1879D61semidirect
441. C61C4×#459semidirect
457. C2×D8C4×D61semidirect
657. D4#14519737semidirect

Maximal subgroups

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

subgroupindex
C2×#168399552
C2×D8×Dic612
C2×#168398422
#214483832
C4×D4×Dic612
#214467442
#214465762
#214464402
#214464362
#214461672
#214458172
#214456672
#102×Dic612
#214456332
C61×#18792
C4×#45961