Finite Group Databasebeta

← #29691216

Subgroups — #29691216

Order 15616.

1296 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839894C211yesmaximal, characteristic
2C4×#14519748C211yesmaximal, characteristic, complemented
3#390×D61C211yesmaximal, characteristic, complemented
4#21446696C211yesmaximal, characteristic, complemented
5#21446692C211yesmaximal, characteristic, complemented
6#21446514C211yesmaximal, characteristic, complemented
7#21446513C211yesmaximal, characteristic, complemented
8#21446447C211yesmaximal, characteristic, complemented
9#21446443C211yesmaximal, characteristic, complemented
10#21446167C211yesmaximal, characteristic, complemented
11#21446133C211yesmaximal, characteristic, complemented
12#21446013C211yesmaximal, characteristic, complemented
13#21445748C211yesmaximal, characteristic, complemented
14#21445580C211yesmaximal, characteristic, complemented
15C61×#1879C211yesmaximal, characteristic, complemented
16C22×D4×D61C2211yescharacteristic
17C22×#11758199C2211yescharacteristic
18C2×#14519748C2211yescharacteristic
19C2×C4×C22⋊D61—21no—
20C2×C4⋊C4×D61C2211yescharacteristic
21C2×C22⋊C4×D61—21no—
22C2×C22⋊C4×D61—21no—
23C2×C42×D61C2211yescharacteristic
24#16839894C418yescomplemented
25C2×#14519709C2211yescharacteristic, complemented
26C2×#14519708C2211yescharacteristic, complemented
27C2×#14519699C2211yescharacteristic
28C2×#14519699C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519698C2211yescharacteristic, complemented
32C2×#14519697C2211yescharacteristic
33C2×#14519689C2211yescharacteristic
34C2×#14519689C2211yescharacteristic
35C2×#14519687C2211yescharacteristic, complemented
36C2×#14519687C2211yescharacteristic, complemented
37#16839665C2211yescharacteristic
38#16839665C2211yescharacteristic, complemented
39#16839664C2211yescharacteristic
40#16839663C2211yescharacteristic
41#16839662—21no—
42#16839662—21no—
43#16839658C2211yescharacteristic, complemented
44#16839650—21no—
45#16839638—21no—
46#16839619C2211yescharacteristic
47C4×C4⋊Dic61C2211yescharacteristic, complemented
48C4×C22⋊Dic61—21no—
49#16839525C2211yescharacteristic, complemented
50#16839524C2211yescharacteristic, complemented
51#16839524C2211yescharacteristic, complemented
52#16839517C2211yescharacteristic, complemented
53C22×D8×C61C2211yescharacteristic
54C2×C4×D4×C61C2211yescharacteristic, complemented
55C2×#102×C61C2211yescharacteristic
56C2×#102×C61C2211yescharacteristic, complemented
57C61×#390C2211yescharacteristic
58C61×#340C2211yescharacteristic, complemented
59C61×#336C2211yescharacteristic, complemented
60C24×D61—21no—
61C22×D244C2311yescharacteristic
62C22×C22⋊D61—21no—
63C22×C22⋊D61—21no—
64C2×D4×D61—22no—
65C2×D4×D61—41no—
66C2×D4×D61—41no—
67C2×D4×D61—41no—
68C2×D4×D61—41no—
69C2×D4×D61C2×C414yescomplemented
70C22×C4×D61—21no—
71C22×C4×D61D411yescharacteristic
72C22×C4×D61D411yescharacteristic
73C22×C4×D61C2311yescharacteristic
74C2×#11758199—41no—
75C2×#11758199—41no—
76C2×#11758199C2×C414yescomplemented
77C22×#92418C2311yescharacteristic
78C22×#92418C2311yescharacteristic
79#14519748—22no—
80#14519748C2×C414yes—
81C4×C22⋊D61—44no—
82C2×C4⋊Dic61C2311yescharacteristic
83C2×C4⋊Dic61C2311yescharacteristic
84C2×C4⋊Dic61C2311yescharacteristic
85C2×#11758196—21no—
86C2×#11758196—21no—
87C4⋊C4×D61—41no—
88C4⋊C4×D61—41no—
89C2×C22⋊Dic61—21no—
90C2×C22⋊Dic61—21no—
91C2×C22⋊Dic61—21no—
92C2×C22⋊Dic61—21no—
93C2×C22⋊Dic61—21no—
94C2×#11758198—21no—
95C2×#11758198—21no—
96C2×#11758198—21no—
97C2×#11758198—21no—
98C2×#11758198—21no—
99C22⋊C4×D61—44no—
100C22⋊C4×D61—44no—
101C2×C4×Dic61—21no—
102C2×C4×Dic61D411yescharacteristic
103C2×C4×Dic61D411yescharacteristic
104C2×C4×Dic61C2311yescharacteristic
105C42×D61—41no—
106C42×D61—41no—
107#14519709—41no—
108#14519708—41no—
109#14519699—41no—
110#14519699C2×C414yescomplemented
111#14519698—41no—
112#14519698—41no—
113#14519698C2×C414yescomplemented
114#14519697—41no—
115#14519689—22no—
116#14519689C2×C414yescomplemented
117#14519687—41no—
118#14519687—41no—
119#14519684—21no—
120#14519684—21no—
121#14519684—21no—
122C22×D4×C61C2311yescharacteristic
123C22×D4×C61C2311yescharacteristic
124C23×C4×C61—21no—
125C2×D8×C61—41no—
126C2×D8×C61—41no—
127C2×D8×C61C2×C414yescomplemented
128C22×C8×C61C2311yescharacteristic
129C22×C8×C61C2311yescharacteristic
130C4×D4×C61—41no—
131C4×D4×C61—41no—
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—41no—
139#102×C61—41no—
140C24×C61—21no—
141C24×C61—21no—
142C23×D61—21no—
143C23×D61—24no—
144C23×D61—42no—
145C23×D61—42no—
146C23×D61—42no—
147C23×D61—42no—
148C23×D61—42no—
149C23×D61—42no—
150C23×D61C2×D411yescharacteristic
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—21no—
159C2×D4×C61—21no—
160C2×D4×C61—21no—
161C2×D4×C61C22×C412yes—
162C2×D4×C61C22×C412yes—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—42no—
166C22×C4×C61—42no—
167C22×C4×C61—42no—
168C22×C4×C61C2×D411yescharacteristic
169C22×C4×C61C2×D411yescharacteristic
170C22×C4×C61C2411yescharacteristic
171C2×C22⋊D61—24no—
172C2×C22⋊D61—24no—
173C2×C22⋊D61—42no—
174C2×C22⋊D61—42no—
175C2×C22⋊D61—42no—
176C2×C22⋊D61—42no—
177C22×Dic61—21no—
178C22×Dic61—21no—
179C22×Dic61—21no—
180C22×Dic61C2×D411yescharacteristic
181C22×Dic61C2×D411yescharacteristic
182C22×Dic61C2×D411yescharacteristic
183D4×D61—44no—
184D4×D61—44no—
185D4×D61—44no—
186D4×D61—44no—
187C2×D244—21no—
188C2×D244—21no—
189C2×D244—21no—
190C2×D244—21no—
191C2×D244—21no—
192C2×D244C22×C412yes—
193C2×C4×D61—21no—
194C2×C4×D61—21no—
195C2×C4×D61—21no—
196C2×C4×D61—21no—
197C2×C4×D61—22no—
198C2×C4×D61—22no—
199C2×C4×D61—22no—
200C2×C4×D61—41no—
201C2×C4×D61—41no—
202C2×C4×D61—41no—
203C2×C4×D61—42no—
204C2×C4×D61—42no—
205C2×C4×D61—42no—
206C2×C4×D61C22×C412yes—
207C2×C4×D61#4112yes—
208D8×C61—44no—
209C2×C8×C61—21no—
210C2×C8×C61—21no—
211C2×C8×C61—21no—
212C2×C8×C61—21no—
213C2×C8×C61—21no—
214C2×C8×C61C22×C412yes—
215C4⋊C4×C61—21no—
216C4⋊C4×C61—21no—
217C4⋊C4×C61—21no—
218C4⋊C4×C61—21no—
219C22⋊C4×C61—42no—
220C22⋊C4×C61—42no—
221C22⋊C4×C61—42no—
222C42×C61—21no—
223C42×C61—21no—
224C22⋊Dic61—24no—
225C22⋊Dic61—42no—
226C22⋊Dic61—42no—
227C22⋊Dic61—42no—
228C22⋊Dic61—42no—
229#11758199—44no—
230#11758198—42no—
231#11758198—42no—
232#11758198—42no—
233#11758198—42no—
234#11758198—42no—
235C4⋊Dic61—21no—
236C4⋊Dic61—21no—
237C4⋊Dic61—21no—
238C4⋊Dic61—21no—
239C4⋊Dic61—21no—
240C4⋊Dic61C22×C412yes—
241#11758196—42no—
242#11758196—42no—
243C4×Dic61—21no—
244C4×Dic61—21no—
245C4×Dic61—41no—
246C4×Dic61—41no—
247C4×Dic61—42no—
248C2×#92418—21no—
249C2×#92418—21no—
250C2×#92418—21no—
251C2×#92418—21no—
252C2×#92418—21no—
253C2×#92418C22×C412yes—
254C23×C61—22no—
255C23×C61—22no—
256C23×C61—41no—
257C23×C61—41no—
258C23×C61—41no—
259C23×C61—41no—
260C23×C61—41no—
261C23×C61—41no—
262C23×C61—41no—
263C23×C61—41no—
264C23×C61—41no—
265C23×C61—41no—
266C23×C61—41no—
267C23×C61—41no—
268C23×C61C22×D411yescharacteristic
269C22×D61—21no—
270C22×D61—21no—
271C22×D61—21no—
272C22×D61—21no—
273C22×D61—22no—
274C22×D61—48no—
275C22×D61—48no—
276C22×D61—41no—
277C22×D61—41no—
278C22×D61—41no—
279C22×D61—41no—
280C22×D61—41no—
281C22×D61—41no—
282C22×D61—48no—
283C22×D61—84no—
284C22×D61—84no—
285C22×D61—84no—
286C22×D61—84no—
287C22×D61C4×D412yes—
288C22×D61AGL(1,ℤ/8)12yes—
289C22×D61AGL(1,ℤ/8)12yes—
290D4×C61—22no—
291D4×C61—22no—
292D4×C61—22no—
293D4×C61—22no—
294D4×C61—41no—
295D4×C61—41no—
296D4×C61—41no—
297D4×C61—41no—
298C2×C4×C61—21no—
299C2×C4×C61—21no—
300C2×C4×C61—21no—
301C2×C4×C61—21no—
302C2×C4×C61—21no—
303C2×C4×C61—41no—
304C2×C4×C61—41no—
305C2×C4×C61—41no—
306C2×C4×C61—41no—
307C2×C4×C61—41no—
308C2×C4×C61—41no—
309C2×C4×C61—84no—
310C2×C4×C61AGL(1,ℤ/8)12yes—
311C2×C4×C61C23×C411yescharacteristic
312C2×C4×C61C2×#4111yescharacteristic
313C2×C4×C61H(5,𝔽2)11yescharacteristic
314C2×C4×C61H(5,𝔽2)11yescharacteristic
315C2×C4×C61H(5,𝔽2)11yescharacteristic
316C2×C4×C61H(5,𝔽2)11yescharacteristic
317C22⋊D61—48no—
318C22⋊D61—48no—
319C2×Dic61—21no—
320C2×Dic61—21no—
321C2×Dic61—22no—
322C2×Dic61—21no—
323C2×Dic61—21no—
324C2×Dic61—21no—
325C2×Dic61—21no—
326C2×Dic61—21no—
327C2×Dic61—21no—
328C2×Dic61—41no—
329C2×Dic61—41no—
330C2×Dic61—41no—
331C2×Dic61—41no—
332C2×Dic61—41no—
333C2×Dic61—41no—
334C2×Dic61—41no—
335C2×Dic61—41no—
336C2×Dic61C4×D412yes—
337D244—22no—
338D244—22no—
339D244—41no—
340D244—41no—
341C4×D61—22no—
342C4×D61—22no—
343C4×D61—22no—
344C4×D61—22no—
345C4×D61—44no—
346C4×D61—44no—
347C4×D61—84no—
348C8×C61—22no—
349C8×C61—41no—
350#92418—22no—
351#92418—41no—
352#22046—611nomaximal, Sylow
353C22×C61—42no—
354C22×C61—42no—
355C22×C61—42no—
356C22×C61—42no—
357C22×C61—42no—
358C22×C61—42no—
359C22×C61—81no—
360C22×C61—81no—
361C22×C61—81no—
362C22×C61—81no—
363C22×C61—81no—
364C22×C61—81no—
365C22×C61—81no—
366C22×C61—81no—
367C22×C61C2×C4×D411yescharacteristic
368C22×C61#53411yescharacteristic
369C22×C61#53511yescharacteristic
370C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
371C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
372C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
373C22×C61#57511yescharacteristic
374C2×D61—22no—
375C2×D61—22no—
376C2×D61—22no—
377C2×D61—22no—
378C2×D61—22no—
379C2×D61—22no—
380C2×D61—42no—
381C2×D61—42no—
382C2×D61—42no—
383C2×D61—816no—
384C2×D61—81no—
385C2×D61—81no—
386C2×D61—81no—
387C2×D61—81no—
388C2×D61#44214yes—
389C4×C61—22no—
390C4×C61—41no—
391C4×C61—81no—
392C4×C61—81no—
393C4×C61#51811yescharacteristic
394C4×C61#51811yescharacteristic
395C4×C61#53811yescharacteristic
396C4×C61#53811yescharacteristic
397Dic61—22no—
398Dic61—41no—
399Dic61—41no—
400Dic61—42no—
401Dic61—81no—
402Dic61—81no—
403C2×#447—611no—
404C4×#121—611no—
405C2×#390—611no—
406#1972—611no—
407#1972—611no—
408#1936—611no—
409#1936—611no—
410#1926—611no—
411#1926—611no—
412#1879—611no—
413#1879D6111yescharacteristic, complemented
414#1874—611no—
415#1853—611no—
416#1786—611no—
417#1749—611no—
418C2×C61—82no—
419C2×C61—82no—
420C2×C61#232111yescharacteristic
421C2×C61C2×#44211yescharacteristic
422C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
423C2×C61#319211yescharacteristic
424C2×C61#319411yescharacteristic
425C2×C61#321311yescharacteristic
426C2×C61#321711yescharacteristic
427D61—24no—
428D61—82no—
429C23×D4—611no—
430C22×D8—611no—
431C22×D8C2×D6111yescharacteristic
432C2×#121—611no—
433C2×C4×D4—1221no—
434C2×C4×D4C2×D6111yescharacteristic, complemented
435C22×C4⋊C4—611no—
436C22×C22⋊C4—1221no—
437C22×C22⋊C4—1221no—
438C22×C42—611no—
439#447—618no—
440C2×#106—611no—
441C2×#106—611no—
442C2×#102—611no—
443C2×#102—611no—
444C2×#102—611no—
445C2×#102—611no—
446C2×#102—611no—
447C2×#102—611no—
448C2×#102C2×D6111yescharacteristic
449C2×#102C2×D6111yescharacteristic, complemented
450C2×C22⋊C8—611no—
451C2×C22⋊C8—611no—
452C2×#97—611no—
453C2×#97—611no—
454#390—611no—
455#390—611no—
456#390—611no—
457#390—611no—
458#390—1221no—
459#390—1221no—
460#390C2×D6111yescharacteristic
461#389—611no—
462#388—1221no—
463#386—1221no—
464#380—611no—
465C4×C4⋊C4—611no—
466C4×C22⋊C4—1221no—
467#340—611no—
468#340—611no—
469#340—611no—
470#340C2×D6111yescharacteristic, complemented
471#336—611no—
472#336C2×D6111yescharacteristic, complemented
473C61#2204611yescharacteristic, complemented, Sylow
474C25—1221no—
475C22×D4—614no—
476C22×D4—611no—
477C22×D4—1222no—
478C22×D4—1221no—
479C22×D4—1221no—
480C22×D4—2441no—
481C22×D4—2441no—
482C22×D4—2441no—
483C22×D4—2441no—
484C22×D4C22×D6111yescharacteristic
485C22×D4C22×D6111yescharacteristic
486C23×C4—21no—
487C23×C4—611no—
488C23×C4—611no—
489C23×C4—611no—
490C23×C4—1221no—
491C2×D8—41no—
492C2×D8—41no—
493C2×D8—614no—
494C2×D8—2441no—
495C2×D8—2441no—
496C2×D8C4×D6114yescomplemented
497C22×C8—611no—
498C22×C8—611no—
499C22×C8C22×D6111yescharacteristic
500C22×C8C22×D6111yescharacteristic
501#121—614no—
502#121—1222no—
503C4×D4—41no—
504C4×D4—41no—
505C4×D4—2444no—
506C2×C4⋊C4—611no—
507C2×C4⋊C4—611no—
508C2×C4⋊C4—611no—
509C2×C4⋊C4—1221no—
510C2×C4⋊C4—1221no—
511C2×C4⋊C4—2441no—
512C2×C4⋊C4—2441no—
513C2×C4⋊C4C22×D6111yescharacteristic
514C2×C4⋊C4C22×D6111yescharacteristic
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—1221no—
519C2×C22⋊C4—1221no—
520C2×C22⋊C4—1221no—
521C2×C22⋊C4—1221no—
522C2×C22⋊C4—1221no—
523C2×C22⋊C4—1221no—
524C2×C22⋊C4—1221no—
525C2×C22⋊C4—1221no—
526C2×C22⋊C4—1221no—
527C2×C22⋊C4—1221no—
528C2×C22⋊C4—2444no—
529C2×C22⋊C4—2444no—
530C2×C42—611no—
531C2×C42—611no—
532C2×C42—611no—
533C2×C42—1221no—
534C2×C42—2441no—
535C2×C42—2441no—
536C2×C42C22×D6111yescharacteristic
537#106—2441no—
538#106—2441no—
539#102—41no—
540#102—41no—
541#102—614no—
542#102—614no—
543#102—2441no—
544#102—2441no—
545#102—2441no—
546#102—2441no—
547C22⋊C8—614no—
548C22⋊C8—1222no—
549#97—2441no—
550#97—2441no—
551#95—1221no—
552#95—1221no—
553#95—1221no—
554C24—21no—
555C24—21no—
556C24—611no—
557C24—1224no—
558C24—1221no—
559C24—2442no—
560C24—2442no—
561C24—2442no—
562C24—2442no—
563C24—2442no—
564C24—2442no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—612no—
576C2×D4—1224no—
577C2×D4—1224no—
578C2×D4—1221no—
579C2×D4—1221no—
580C2×D4—1221no—
581C2×D4—1221no—
582C2×D4—1221no—
583C2×D4—2444no—
584C2×D4—2444no—
585C2×D4—2444no—
586C2×D4—2444no—
587C2×D4—2442no—
588C2×D4—2442no—
589C2×D4—2442no—
590C2×D4—2442no—
591C2×D4C2×C4×D6112yes—
592C2×D4C2×C4×D6112yes—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—611no—
599C22×C4—612no—
600C22×C4—612no—
601C22×C4—611no—
602C22×C4—611no—
603C22×C4—1222no—
604C22×C4—1222no—
605C22×C4—1221no—
606C22×C4—1221no—
607C22×C4—1221no—
608C22×C4—1221no—
609C22×C4—1221no—
610C22×C4—1222no—
611C22×C4—1221no—
612C22×C4—1221no—
613C22×C4—2441no—
614C22×C4—2441no—
615C22×C4—2441no—
616C22×C4—2442no—
617C22×C4—2442no—
618C22×C4—2442no—
619C22×C4D4×D6111yescharacteristic
620C22×C4D4×D6111yescharacteristic
621C22×C4C23×D6111yescharacteristic
622D8—44no—
623D8—2444no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—612no—
630C2×C8—1221no—
631C2×C8—1221no—
632C2×C8—1221no—
633C2×C8—1221no—
634C2×C8—1221no—
635C2×C8C2×C4×D6112yes—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—612no—
641C4⋊C4—1221no—
642C4⋊C4—1221no—
643C4⋊C4—1221no—
644C4⋊C4—1221no—
645C4⋊C4—1221no—
646C4⋊C4—2442no—
647C4⋊C4—2442no—
648C22⋊C4—42no—
649C22⋊C4—42no—
650C22⋊C4—42no—
651C22⋊C4—1224no—
652C22⋊C4—2442no—
653C22⋊C4—2442no—
654C22⋊C4—2442no—
655C22⋊C4—2442no—
656C22⋊C4—2442no—
657C22⋊C4—2442no—
658C22⋊C4—2442no—
659C22⋊C4—2442no—
660C22⋊C4—2442no—
661C42—21no—
662C42—21no—
663C42—1221no—
664C42—1221no—
665C42—2441no—
666C42—2441no—
667C42—2442no—
668C23—22no—
669C23—22no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—612no—
683C23—612no—
684C23—612no—
685C23—1221no—
686C23—1221no—
687C23—1221no—
688C23—1221no—
689C23—1222no—
690C23—4884no—
691C23—4884no—
692C23—4884no—
693C23—4884no—
694C23—2448no—
695C23—2448no—
696C23—2448no—
697C23—2441no—
698C23—2441no—
699C23—2441no—
700C23—2441no—
701C23—2441no—
702C23—2441no—
703C23C2×D4×D6111yescharacteristic
704D4—22no—
705D4—22no—
706D4—22no—
707D4—22no—
708D4—41no—
709D4—41no—
710D4—41no—
711D4—41no—
712D4—1222no—
713D4—1222no—
714D4—2448no—
715D4—2448no—
716D4—2441no—
717D4—2441no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—84no—
730C2×C4—612no—
731C2×C4—1221no—
732C2×C4—1221no—
733C2×C4—1222no—
734C2×C4—1222no—
735C2×C4—1222no—
736C2×C4—1222no—
737C2×C4—1222no—
738C2×C4—1221no—
739C2×C4—1221no—
740C2×C4—1221no—
741C2×C4—1221no—
742C2×C4—1221no—
743C2×C4—1221no—
744C2×C4—4884no—
745C2×C4—2444no—
746C2×C4—2444no—
747C2×C4—2441no—
748C2×C4—2441no—
749C2×C4—2441no—
750C2×C4—2441no—
751C2×C4—2441no—
752C2×C4—2441no—
753C2×C4—2441no—
754C2×C4—2441no—
755C2×C4#1451980112yes—
756C2×C4C22×C4×D6111yescharacteristic
757C2×C4#41×D6111yescharacteristic
758C2×C4#1451982211yescharacteristic
759C2×C4#1451982211yescharacteristic
760C2×C4#1451982211yescharacteristic
761C2×C4#1451982311yescharacteristic
762C8—22no—
763C8—41no—
764C8—1222no—
765C8—2441no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—42no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—614no—
781C22—1222no—
782C22—1222no—
783C22—1222no—
784C22—1222no—
785C22—1222no—
786C22—1222no—
787C22—48816no—
788C22—4881no—
789C22—4881no—
790C22—4881no—
791C22—4881no—
792C22—2442no—
793C22—2442no—
794C22—2442no—
795C22C4×D4×D6111yescharacteristic
796C22#1684032211yescharacteristic
797C22#1684032811yescharacteristic
798C22AGL(1,ℤ/8)×D6111yescharacteristic
799C22AGL(1,ℤ/8)×D6111yescharacteristic
800C22C2×#1451980111yescharacteristic
801C22#1684055911yescharacteristic
802C4—22no—
803C4—41no—
804C4—81no—
805C4—81no—
806C4—1222no—
807C4—4881no—
808C4—4881no—
809C4—2442no—
810C4—2441no—
811C4—2441no—
812C4#1684023411yescharacteristic
813C4#1684023511yescharacteristic
814C4#1684034411yescharacteristic
815C4#1684034811yescharacteristic
816C2—82no—
817C2—82no—
818C2—1224no—
819C2—4882no—
820C2#2144847511yescharacteristic
821C2#442×D6111yescharacteristic
822C2C4×#1451980111yescharacteristic
823C2#2145661711yescharacteristic
824C2#2145663111yescharacteristic
825C2#2145680411yescharacteristic
826C2#2145683611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1879C2
socleC23×C61C22×D4
prime radicalC2×#16839894C2
cosocleC22×C4×C61C24
hypercenter#1879D61
hypocenterC61#22046
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. C4×#14519748C2semidirect
3. #390×D61C2semidirect
4. #21446696C2semidirect
5. #21446692C2semidirect
6. #21446514C2semidirect
7. #21446513C2semidirect
8. #21446447C2semidirect
9. #21446443C2semidirect
10. #21446167C2semidirect
11. #21446133C2semidirect
12. #21446013C2semidirect
13. #21445748C2semidirect
14. #21445580C2semidirect
15. C61×#1879C2semidirect
24. #16839894C4semidirect
25. C2×#14519709C22semidirect
26. C2×#14519708C22semidirect
31. C2×#14519698C22semidirect
35. C2×#14519687C22semidirect
36. C2×#14519687C22semidirect
38. #16839665C22semidirect
43. #16839658C22semidirect
47. C4×C4⋊Dic61C22semidirect
49. #16839525C22semidirect
50. #16839524C22semidirect
51. #16839524C22semidirect
52. #16839517C22semidirect
54. C2×C4×D4×C61C22semidirect
56. C2×#102×C61C22semidirect
58. C61×#340C22semidirect
59. C61×#336C22semidirect
69. C2×D4×D61C2×C4semidirect
76. C2×#11758199C2×C4semidirect
110. #14519699C2×C4semidirect
113. #14519698C2×C4semidirect
116. #14519689C2×C4semidirect
127. C2×D8×C61C2×C4semidirect
413. #1879D61semidirect
434. C2×C4×D4C2×D61semidirect
449. C2×#102C2×D61semidirect
470. #340C2×D61semidirect
472. #336C2×D61semidirect
473. C61#22046semidirect
496. C2×D8C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168398942
C4×#145197482
#390×D612
#214466962
#214466922
#214465142
#214465132
#214464472
#214464432
#214461672
#214461332
#214460132
#214457482
#214455802
C61×#18792
#2204661