Finite Group Databasebeta

← #29691219

Subgroups — #29691219

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
2#21448335C211yesmaximal, characteristic, complemented
3#390×D61C211yesmaximal, characteristic, complemented
4#21446694C211yesmaximal, characteristic, complemented
5#21446519C211yesmaximal, characteristic, complemented
6#21446516C211yesmaximal, characteristic, complemented
7#21446449C211yesmaximal, characteristic, complemented
8#21446445C211yesmaximal, characteristic, complemented
9#21446169C211yesmaximal, characteristic, complemented
10#21446165C211yesmaximal, characteristic, complemented
11#21446133C211yesmaximal, characteristic, complemented
12#21446010C211yesmaximal, characteristic, complemented
13#21445748C211yesmaximal, characteristic, complemented
14#21445582C211yesmaximal, characteristic, complemented
15C61×#1972C211yesmaximal, characteristic, complemented
16C22×D4×D61C2211yescharacteristic
17C22×#11758199C2211yescharacteristic
18C2×#14519748C2211yescharacteristic
19C2×D4×Dic61C2211yescharacteristic, complemented
20C2×#14519737—21no—
21C2×C4⋊C4×D61C2211yescharacteristic
22C2×C22⋊C4×D61—21no—
23C2×C22⋊C4×D61—21no—
24C2×C42×D61C2211yescharacteristic
25#16839894C418yescomplemented
26C2×#14519708C2211yescharacteristic, complemented
27C2×#14519699C2211yescharacteristic
28C2×#14519699C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519698C2211yescharacteristic, complemented
32C2×#14519697C2211yescharacteristic
33C2×#14519689C2211yescharacteristic
34C2×#14519689C2211yescharacteristic
35C2×#14519688C2211yescharacteristic, complemented
36#16839665C2211yescharacteristic
37#16839664C2211yescharacteristic
38#16839663C2211yescharacteristic
39#16839662—21no—
40#16839662—21no—
41#16839660C2211yescharacteristic, complemented
42#16839656—21no—
43#16839638—21no—
44#16839619C2211yescharacteristic
45C4⋊C4×Dic61C2211yescharacteristic, complemented
46C22⋊C4×Dic61—21no—
47#16839525C2211yescharacteristic, complemented
48#16839525C2211yescharacteristic, complemented
49#16839524C2211yescharacteristic, complemented
50#16839524C2211yescharacteristic, complemented
51#16839516C2211yescharacteristic, complemented
52#16839516C2211yescharacteristic, complemented
53C22×D8×C61C2211yescharacteristic
54C2×#106×C61C2211yescharacteristic, complemented
55C2×#102×C61C2211yescharacteristic
56C2×#102×C61C2211yescharacteristic, complemented
57C2×#97×C61C2211yescharacteristic, complemented
58C61×#390C2211yescharacteristic
59C61×#390C2211yescharacteristic, 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
70C23×Dic61—21no—
71C22×C4×D61—21no—
72C22×C4×D61D411yescharacteristic
73C22×C4×D61D411yescharacteristic
74C22×C4×D61C2311yescharacteristic
75C2×#11758199—41no—
76C2×#11758199—41no—
77C2×#11758199C2×C414yescomplemented
78C22×#92418C2311yescharacteristic
79C22×#92418C2311yescharacteristic
80#14519748—22no—
81#14519748C2×C414yes—
82D4×Dic61—41no—
83D4×Dic61—41no—
84#14519737—44no—
85C2×C4⋊Dic61C2311yescharacteristic
86C2×C4⋊Dic61C2311yescharacteristic
87C2×C4⋊Dic61C2311yescharacteristic
88C2×#11758196—21no—
89C2×#11758196—21no—
90C4⋊C4×D61—41no—
91C4⋊C4×D61—41no—
92C2×C22⋊Dic61—21no—
93C2×C22⋊Dic61—21no—
94C2×C22⋊Dic61—21no—
95C2×C22⋊Dic61—21no—
96C2×#11758198—21no—
97C2×#11758198—21no—
98C2×#11758198—21no—
99C2×#11758198—21no—
100C2×#11758198—21no—
101C22⋊C4×D61—44no—
102C22⋊C4×D61—44no—
103C2×C4×Dic61—21no—
104C2×C4×Dic61D411yescharacteristic
105C2×C4×Dic61D411yescharacteristic
106C2×C4×Dic61C2311yescharacteristic
107C42×D61—41no—
108C42×D61—41no—
109#14519708—41no—
110#14519699—41no—
111#14519699C2×C414yescomplemented
112#14519698—41no—
113#14519698—41no—
114#14519698C2×C414yescomplemented
115#14519697—41no—
116#14519689—22no—
117#14519689C2×C414yescomplemented
118#14519688—41no—
119#14519684—21no—
120#14519684—21no—
121#14519684—21no—
122C22×D4×C61C2311yescharacteristic
123C22×D4×C61C2311yescharacteristic
124C2×D8×C61—41no—
125C2×D8×C61—41no—
126C2×D8×C61C2×C414yescomplemented
127C22×C8×C61C2311yescharacteristic
128C22×C8×C61C2311yescharacteristic
129C2×C4⋊C4×C61C2311yescharacteristic
130C2×C4⋊C4×C61C2311yescharacteristic
131C2×C22⋊C4×C61—21no—
132C2×C22⋊C4×C61—21no—
133C2×C22⋊C4×C61—21no—
134C2×C22⋊C4×C61—21no—
135C2×C42×C61C2311yescharacteristic
136#106×C61—41no—
137#102×C61—41no—
138#102×C61—41no—
139#97×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×C61C2×D411yescharacteristic
166C22×C4×C61C2×D411yescharacteristic
167C22×C4×C61C2411yescharacteristic
168C2×C22⋊D61—24no—
169C2×C22⋊D61—24no—
170C2×C22⋊D61—42no—
171C2×C22⋊D61—42no—
172C2×C22⋊D61—42no—
173C2×C22⋊D61—42no—
174C22×Dic61—21no—
175C22×Dic61—21no—
176C22×Dic61—21no—
177C22×Dic61—42no—
178C22×Dic61—42no—
179C22×Dic61—42no—
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—
222C22⋊C4×C61—42no—
223C42×C61—21no—
224C42×C61—21no—
225C22⋊Dic61—24no—
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—21no—
304C2×C4×C61—41no—
305C2×C4×C61—41no—
306C2×C4×C61—41no—
307C2×C4×C61—41no—
308C2×C4×C61—41no—
309C2×C4×C61—41no—
310C2×C4×C61C23×C411yescharacteristic
311C2×C4×C61C2×#4111yescharacteristic
312C2×C4×C61H(5,𝔽2)11yescharacteristic
313C2×C4×C61H(5,𝔽2)11yescharacteristic
314C2×C4×C61H(5,𝔽2)11yescharacteristic
315C2×C4×C61H(5,𝔽2)11yescharacteristic
316C22⋊D61—48no—
317C22⋊D61—48no—
318C2×Dic61—21no—
319C2×Dic61—21no—
320C2×Dic61—21no—
321C2×Dic61—21no—
322C2×Dic61—22no—
323C2×Dic61—21no—
324C2×Dic61—21no—
325C2×Dic61—21no—
326C2×Dic61—41no—
327C2×Dic61—41no—
328C2×Dic61—41no—
329C2×Dic61—41no—
330C2×Dic61—41no—
331C2×Dic61—41no—
332C2×Dic61—41no—
333C2×Dic61—41no—
334C2×Dic61—84no—
335C2×Dic61C4×D412yes—
336C2×Dic61AGL(1,ℤ/8)12yes—
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—41no—
390C4×C61—41no—
391C4×C61—81no—
392C4×C61—81no—
393C4×C61#51811yescharacteristic
394C4×C61#51811yescharacteristic
395C4×C61#53811yescharacteristic
396C4×C61#53811yescharacteristic
397Dic61—22no—
398Dic61—22no—
399Dic61—41no—
400Dic61—42no—
401Dic61—81no—
402Dic61—81no—
403C2×#447—611no—
404C4×#121—611no—
405C2×#390—611no—
406#1972—611no—
407#1972D6111yescharacteristic, complemented
408#1936—611no—
409#1936—611no—
410#1926—611no—
411#1926—611no—
412#1879—611no—
413#1879—611no—
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—611no—
434C2×C4×D4—1221no—
435C22×C4⋊C4—611no—
436C22×C22⋊C4—1221no—
437C22×C22⋊C4—1221no—
438C22×C42—611no—
439#447—618no—
440C2×#106—611no—
441C2×#106C2×D6111yescharacteristic, complemented
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×#97C2×D6111yescharacteristic, complemented
454#390—611no—
455#390—611no—
456#390—611no—
457#390—1221no—
458#390—1221no—
459#390C2×D6111yescharacteristic
460#390C2×D6111yescharacteristic, complemented
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#340—611no—
471#336—611no—
472#336—611no—
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—611no—
487C23×C4—611no—
488C23×C4—611no—
489C23×C4—1221no—
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—2441no—
504C4×D4—2441no—
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—21no—
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—41no—
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—41no—
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—611no—
596C22×C4—611no—
597C22×C4—612no—
598C22×C4—612no—
599C22×C4—611no—
600C22×C4—1222no—
601C22×C4—1222no—
602C22×C4—1222no—
603C22×C4—1221no—
604C22×C4—1221no—
605C22×C4—1221no—
606C22×C4—1221no—
607C22×C4—1221no—
608C22×C4—1221no—
609C22×C4—1221no—
610C22×C4—2441no—
611C22×C4—2441no—
612C22×C4—2441no—
613C22×C4—2442no—
614C22×C4—2442no—
615C22×C4—2442no—
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—42no—
652C22⋊C4—1224no—
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—21no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—612no—
731C2×C4—612no—
732C2×C4—1221no—
733C2×C4—1221no—
734C2×C4—1221no—
735C2×C4—1221no—
736C2×C4—1222no—
737C2×C4—1222no—
738C2×C4—1222no—
739C2×C4—1222no—
740C2×C4—1222no—
741C2×C4—1221no—
742C2×C4—1221no—
743C2×C4—1221no—
744C2×C4—4884no—
745C2×C4—4884no—
746C2×C4—2444no—
747C2×C4—2444no—
748C2×C4—2441no—
749C2×C4—2441no—
750C2×C4—2441no—
751C2×C4—2441no—
752C2×C4—2441no—
753C2×C4—2441no—
754C2×C4—2441no—
755C2×C4—2441no—
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#1684032011yescharacteristic
797C22#1684032511yescharacteristic
798C22AGL(1,ℤ/8)×D6111yescharacteristic
799C22AGL(1,ℤ/8)×D6111yescharacteristic
800C22AGL(1,ℤ/8)×D6111yescharacteristic
801C22#1684055811yescharacteristic
802C4—41no—
803C4—41no—
804C4—81no—
805C4—81no—
806C4—1222no—
807C4—1222no—
808C4—4881no—
809C4—4881no—
810C4—2442no—
811C4—2441no—
812C4#1684023411yescharacteristic
813C4#1684023511yescharacteristic
814C4#1684034411yescharacteristic
815C4#1684034611yescharacteristic
816C2—82no—
817C2—82no—
818C2—1224no—
819C2—4882no—
820C2#2144847811yescharacteristic
821C2#442×D6111yescharacteristic
822C2#2145463011yescharacteristic
823C2#2145661511yescharacteristic
824C2#2145662811yescharacteristic
825C2#2145680111yescharacteristic
826C2#2145683311yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1972C2
socleC23×C61C22×D4
prime radicalC2×#16839894C2
cosocleC22×C4×C61C24
hypercenter#1972D61
hypocenterC61#22046
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1972

Complements

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

NH ≅ G/Ntype
2. #21448335C2semidirect
3. #390×D61C2semidirect
4. #21446694C2semidirect
5. #21446519C2semidirect
6. #21446516C2semidirect
7. #21446449C2semidirect
8. #21446445C2semidirect
9. #21446169C2semidirect
10. #21446165C2semidirect
11. #21446133C2semidirect
12. #21446010C2semidirect
13. #21445748C2semidirect
14. #21445582C2semidirect
15. C61×#1972C2semidirect
19. C2×D4×Dic61C22semidirect
25. #16839894C4semidirect
26. C2×#14519708C22semidirect
31. C2×#14519698C22semidirect
35. C2×#14519688C22semidirect
41. #16839660C22semidirect
45. C4⋊C4×Dic61C22semidirect
47. #16839525C22semidirect
48. #16839525C22semidirect
49. #16839524C22semidirect
50. #16839524C22semidirect
51. #16839516C22semidirect
52. #16839516C22semidirect
54. C2×#106×C61C22semidirect
56. C2×#102×C61C22semidirect
57. C2×#97×C61C22semidirect
59. C61×#390C22semidirect
69. C2×D4×D61C2×C4semidirect
77. C2×#11758199C2×C4semidirect
111. #14519699C2×C4semidirect
114. #14519698C2×C4semidirect
117. #14519689C2×C4semidirect
126. C2×D8×C61C2×C4semidirect
407. #1972D61semidirect
441. C2×#106C2×D61semidirect
449. C2×#102C2×D61semidirect
453. C2×#97C2×D61semidirect
460. #390C2×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
#214483352
#390×D612
#214466942
#214465192
#214465162
#214464492
#214464452
#214461692
#214461652
#214461332
#214460102
#214457482
#214455822
C61×#19722
#2204661