Finite Group Databasebeta

← #29689062

Subgroups — #29689062

Order 15616.

1882 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#121×D61C211yesmaximal, characteristic
2C2×#16839724C211yesmaximal, characteristic, complemented
3C2×#16839619C211yesmaximal, characteristic, complemented
4#21446256C212yesmaximal, complemented
5#21446254C212yesmaximal, complemented
6#21446137C211yesmaximal, characteristic, complemented
7#21446136C211yesmaximal, characteristic, complemented
8#21446134C211yesmaximal, characteristic, complemented
9#21445908C212yesmaximal, complemented
10#21445748C212yesmaximal, complemented
11C61×#1874C211yesmaximal, characteristic, complemented
12C22×D4×D61—21no—
13C22×D4×D61C2211yescharacteristic
14C23×C4×D61C2211yescharacteristic
15C22×#11758189C2212yescomplemented
16C2×#14519752C2211yescharacteristic
17C2×#14519751C2211yescharacteristic
18C2×#14519750—21no—
19C2×#14519749—21no—
20C2×#14519748C2211yescharacteristic
21#121×D61—24no—
22#121×D61C418yescomplemented
23C22×C4⋊Dic61C2211yescharacteristic, complemented
24C2×C4⋊C4×D61C2211yescharacteristic
25C22×#11758198—21no—
26C2×C22⋊C4×D61—21no—
27C2×#14519699C2212yescomplemented
28C2×#14519698C2212yescomplemented
29C2×#14519697C2212yescomplemented
30#16839724—24no—
31C2×C22⋊#92418C2211yescharacteristic, complemented
32C2×#14519689C2212yes—
33#16839619—21no—
34#16839619—21no—
35#16839619C2212yes—
36#16839619C2212yescomplemented
37C2×#14519684—21no—
38#16839525C2212yescomplemented
39#16839524C2212yescomplemented
40#16839524C2212yescomplemented
41C2×#121×C61C2211yescharacteristic
42C22×C4⋊C4×C61C2211yescharacteristic, complemented
43C2×#102×C61C2212yescomplemented
44C2×C22⋊C8×C61C2211yescharacteristic, complemented
45C61×#340C2212yescomplemented
46C24×D61—21no—
47C24×D61D411yescharacteristic
48C22×D244—21no—
49C22×D244C2311yescharacteristic
50C22×C22⋊D61—21no—
51C22×C22⋊D61—21no—
52C22×C22⋊D61—21no—
53C2×D4×D61—28no—
54C2×D4×D61—22no—
55C2×D4×D61—42no—
56C2×D4×D61—42no—
57C2×D4×D61—44no—
58C2×D4×D61—44no—
59C2×D4×D61C2×C414yescomplemented
60C23×Dic61—21no—
61C23×Dic61D411yescharacteristic
62C22×C4×D61—21no—
63C22×C4×D61—42no—
64C22×C4×D61—42no—
65C22×C4×D61C2×C414yes—
66C22×C4×D61D411yescharacteristic
67C22×C4×D61D411yescharacteristic
68C22×C4×D61D414yes—
69C22×C4×D61C2311yescharacteristic
70C22×C4×D61C2311yescharacteristic
71C2×#11758189—24no—
72C2×#11758189—42no—
73C2×#11758189—42no—
74C22×#92418C2312yes—
75#14519752—22no—
76#14519752C2×C414yescomplemented
77#14519751—22no—
78#14519751C2×C414yes—
79#14519750—28no—
80#14519749—28no—
81#14519748—22no—
82#14519748C2×C414yescomplemented
83C2×C4⋊Dic61—21no—
84C2×C4⋊Dic61—42no—
85C2×C4⋊Dic61C2312yes—
86C2×C4⋊Dic61C2311yescharacteristic
87C2×#11758196—21no—
88C4⋊C4×D61—22no—
89C4⋊C4×D61C2×C414yescomplemented
90C2×C22⋊Dic61—21no—
91C2×#11758198—21no—
92C2×#11758198—21no—
93C2×#11758198—22no—
94C2×#11758198—22no—
95C2×#11758198—44no—
96C22⋊C4×D61—28no—
97#14519699—42no—
98#14519698—42no—
99#14519697—42no—
100C22⋊#92418—22no—
101#14519689—24no—
102#14519684—22no—
103#14519684—22no—
104C22×D4×C61—21no—
105C22×D4×C61C2311yescharacteristic
106C23×C4×C61—21no—
107C23×C4×C61C2311yescharacteristic
108C22×C8×C61C2312yes—
109#121×C61—22no—
110#121×C61C2×C414yes—
111C2×C4⋊C4×C61—21no—
112C2×C4⋊C4×C61—42no—
113C2×C4⋊C4×C61C2312yes—
114C2×C4⋊C4×C61C2311yescharacteristic
115C2×C22⋊C4×C61—21no—
116#102×C61—42no—
117C22⋊C8×C61—22no—
118C24×C61—21no—
119C24×C61C2×D411yescharacteristic
120C23×D61—22no—
121C23×D61—22no—
122C23×D61—22no—
123C23×D61—22no—
124C23×D61—21no—
125C23×D61—24no—
126C23×D61—41no—
127C23×D61—41no—
128C23×D61—42no—
129C23×D61—42no—
130C23×D61—42no—
131C23×D61—42no—
132C23×D61—42no—
133C23×D61—42no—
134C23×D61C22⋊C414yes—
135C23×D61C2×D411yescharacteristic
136C23×D61C2×D411yescharacteristic
137C2×D4×C61—24no—
138C2×D4×C61—21no—
139C2×D4×C61—22no—
140C2×D4×C61—22no—
141C2×D4×C61—42no—
142C2×D4×C61—42no—
143C2×D4×C61C22×C412yes—
144C22×C4×C61—22no—
145C22×C4×C61—22no—
146C22×C4×C61—21no—
147C22×C4×C61—22no—
148C22×C4×C61—42no—
149C22×C4×C61—42no—
150C22×C4×C61—42no—
151C22×C4×C61C22×C412yes—
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2×D412yes—
154C22×C4×C61C2411yescharacteristic
155C2×C22⋊D61—24no—
156C2×C22⋊D61—24no—
157C2×C22⋊D61—24no—
158C2×C22⋊D61—42no—
159C2×C22⋊D61—42no—
160C2×C22⋊D61—42no—
161C2×C22⋊D61—42no—
162C2×C22⋊D61—42no—
163C2×C22⋊D61—42no—
164C22×Dic61—21no—
165C22×Dic61—22no—
166C22×Dic61—41no—
167C22×Dic61—41no—
168C22×Dic61—42no—
169C22×Dic61—42no—
170C22×Dic61—42no—
171C22×Dic61C22⋊C414yes—
172C22×Dic61C2×D411yescharacteristic
173C22×Dic61C2×D411yescharacteristic
174D4×D61—48no—
175D4×D61—48no—
176D4×D61—432no—
177C2×D244—22no—
178C2×D244—22no—
179C2×D244—24no—
180C2×D244—21no—
181C2×D244—42no—
182C2×D244—42no—
183C2×D244C22×C412yes—
184C2×C4×D61—22no—
185C2×C4×D61—22no—
186C2×C4×D61—22no—
187C2×C4×D61—22no—
188C2×C4×D61—24no—
189C2×C4×D61—48no—
190C2×C4×D61—48no—
191C2×C4×D61—41no—
192C2×C4×D61—41no—
193C2×C4×D61—41no—
194C2×C4×D61—41no—
195C2×C4×D61—42no—
196C2×C4×D61—42no—
197C2×C4×D61C22⋊C414yes—
198C2×C4×D61C22⋊C414yes—
199C2×C4×D61C22×C412yes—
200C2×C4×D61C22×C412yes—
201C2×C4×D61C2×D412yes—
202C2×C4×D61C2×D412yes—
203C2×C8×C61—22no—
204C2×C8×C61—22no—
205C2×C8×C61—22no—
206C4⋊C4×C61—21no—
207C4⋊C4×C61—22no—
208C4⋊C4×C61—22no—
209C4⋊C4×C61—42no—
210C4⋊C4×C61C22×C412yes—
211C22⋊C4×C61—24no—
212C22⋊Dic61—24no—
213#11758198—24no—
214#11758198—24no—
215#11758198—44no—
216#11758198—44no—
217C4⋊Dic61—21no—
218C4⋊Dic61—22no—
219C4⋊Dic61—22no—
220C4⋊Dic61—42no—
221C4⋊Dic61C22×C412yes—
222#11758196—24no—
223C2×#92418—22no—
224C2×#92418—22no—
225C2×#92418—22no—
226#11758189—48no—
227C23×C61—21no—
228C23×C61—21no—
229C23×C61—21no—
230C23×C61—21no—
231C23×C61—22no—
232C23×C61—41no—
233C23×C61—41no—
234C23×C61—41no—
235C23×C61—41no—
236C23×C61—41no—
237C23×C61—41no—
238C23×C61C2×C22⋊C412yes—
239C23×C61AGL(1,ℤ/8)12yes—
240C23×C61AGL(1,ℤ/8)12yes—
241C23×C61C22×D411yescharacteristic
242C22×D61—21no—
243C22×D61—21no—
244C22×D61—21no—
245C22×D61—21no—
246C22×D61—21no—
247C22×D61—21no—
248C22×D61—21no—
249C22×D61—21no—
250C22×D61—21no—
251C22×D61—21no—
252C22×D61—28no—
253C22×D61—28no—
254C22×D61—22no—
255C22×D61—44no—
256C22×D61—44no—
257C22×D61—44no—
258C22×D61—44no—
259C22×D61—44no—
260C22×D61—48no—
261C22×D61—48no—
262C22×D61—41no—
263C22×D61—41no—
264C22×D61—41no—
265C22×D61—41no—
266C22×D61—41no—
267C22×D61—41no—
268C22×D61—48no—
269C22×D61—84no—
270C22×D61—84no—
271C22×D61—84no—
272C22×D61—84no—
273C22×D61C2×C22⋊C412yes—
274C22×D61C2×C22⋊C412yes—
275C22×D61AGL(1,ℤ/8)12yes—
276C22×D61#13712yes—
277D4×C61—24no—
278D4×C61—48no—
279D4×C61—42no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—24no—
283C2×C4×C61—24no—
284C2×C4×C61—22no—
285C2×C4×C61—41no—
286C2×C4×C61—41no—
287C2×C4×C61—42no—
288C2×C4×C61—42no—
289C2×C4×C61—42no—
290C2×C4×C61—84no—
291C2×C4×C61C2×C22⋊C412yes—
292C2×C4×C61C23×C411yescharacteristic
293C2×C4×C61C22×D411yescharacteristic
294C2×C4×C61H(5,𝔽2)12yes—
295C2×C4×C61H(5,𝔽2)12yes—
296C22⋊D61—48no—
297C22⋊D61—48no—
298C22⋊D61—48no—
299C2×Dic61—21no—
300C2×Dic61—21no—
301C2×Dic61—21no—
302C2×Dic61—21no—
303C2×Dic61—22no—
304C2×Dic61—44no—
305C2×Dic61—41no—
306C2×Dic61—41no—
307C2×Dic61—42no—
308C2×Dic61—42no—
309C2×Dic61—42no—
310C2×Dic61—84no—
311C2×Dic61C2×C22⋊C412yes—
312C2×Dic61C2×C22⋊C412yes—
313D244—24no—
314D244—48no—
315D244—42no—
316C4×D61—24no—
317C4×D61—24no—
318C4×D61—24no—
319C4×D61—24no—
320C4×D61—44no—
321C4×D61—44no—
322C4×D61—48no—
323C8×C61—42no—
324#92418—42no—
325#21764—611nomaximal, Sylow
326C22×C61—22no—
327C22×C61—22no—
328C22×C61—22no—
329C22×C61—22no—
330C22×C61—22no—
331C22×C61—22no—
332C22×C61—42no—
333C22×C61—42no—
334C22×C61—42no—
335C22×C61—81no—
336C22×C61—81no—
337C22×C61—81no—
338C22×C61—81no—
339C22×C61#41814yes—
340C22×C61C22×C22⋊C411yescharacteristic
341C22×C61#53411yescharacteristic
342C22×C61#53411yescharacteristic
343C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
344C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
345C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
346C22×C61C2×#13711yescharacteristic
347C2×D61—22no—
348C2×D61—22no—
349C2×D61—22no—
350C2×D61—22no—
351C2×D61—22no—
352C2×D61—22no—
353C2×D61—22no—
354C2×D61—22no—
355C2×D61—22no—
356C2×D61—416no—
357C2×D61—41no—
358C2×D61—41no—
359C2×D61—41no—
360C2×D61—41no—
361C2×D61—42no—
362C2×D61—42no—
363C2×D61—42no—
364C2×D61—816no—
365C2×D61—81no—
366C2×D61—81no—
367C2×D61—81no—
368C2×D61—81no—
369C2×D61#41714yes—
370C4×C61—22no—
371C4×C61—42no—
372C4×C61—82no—
373C4×C61#51812yes—
374C4×C61#53412yes—
375Dic61—22no—
376Dic61—22no—
377Dic61—42no—
378Dic61—82no—
379C22×#121—611no—
380C2×#407—611no—
381C2×#380—611no—
382#1895—612no—
383#1895—612no—
384#1874—611no—
385#1874—611no—
386#1874—611no—
387#1874D6111yescharacteristic, complemented
388#1824—612no—
389#1786—612no—
390C2×C61—24no—
391C2×C61—82no—
392C2×C61#230811yescharacteristic
393C2×C61C2×#41811yescharacteristic
394C2×C61C2×#41711yescharacteristic
395C2×C61#319211yescharacteristic
396C2×C61#319211yescharacteristic
397C2×C61#319311yescharacteristic
398C2×C61#319311yescharacteristic
399D61—24no—
400D61—42no—
401D61—82no—
402C23×D4—611no—
403C23×D4—1221no—
404C24×C4—611no—
405C22×M16—612no—
406C2×#121—611no—
407C2×#121—611no—
408C2×#121—618no—
409C2×#121—611no—
410C2×#121—1221no—
411C2×#121—1224no—
412C2×#121—1221no—
413C2×#121C2×D6111yescharacteristic
414C22×C4⋊C4—611no—
415C22×C4⋊C4—611no—
416C22×C4⋊C4C2×D6111yescharacteristic, complemented
417C22×C22⋊C4—1221no—
418C22×C22⋊C4—1221no—
419C2×#102—612no—
420C2×#102—612no—
421C2×#102—612no—
422C2×#102C2×D6112yescomplemented
423#407—1224no—
424C2×C22⋊C8—611no—
425C2×C22⋊C8—612no—
426C2×C22⋊C8C2×D6111yescharacteristic, complemented
427#380—612no—
428#380—612no—
429#380—1221no—
430#380—1221no—
431C2×#95—1221no—
432#340—612no—
433#340—612no—
434#340—612no—
435#340C2×D6112yescomplemented
436C61#2176411yescharacteristic, complemented, Sylow
437C25—611no—
438C25—1221no—
439C22×D4—21no—
440C22×D4—614no—
441C22×D4—611no—
442C22×D4—1221no—
443C22×D4—1222no—
444C22×D4—1221no—
445C22×D4—1228no—
446C22×D4—1221no—
447C22×D4—1221no—
448C22×D4—2442no—
449C22×D4—2442no—
450C22×D4—2444no—
451C22×D4—2444no—
452C22×D4C22×D6111yescharacteristic
453C23×C4—21no—
454C23×C4—611no—
455C23×C4—611no—
456C23×C4—611no—
457C23×C4—614no—
458C23×C4—611no—
459C23×C4—611no—
460C23×C4—614no—
461C23×C4—1221no—
462C23×C4—1221no—
463C23×C4—2442no—
464C23×C4—2442no—
465C23×C4C22×D6111yescharacteristic
466C2×M16—1224no—
467C2×M16—2442no—
468C2×M16—2442no—
469C22×C8—612no—
470C22×C8C22×D6112yes—
471#121—22no—
472#121—614no—
473#121—614no—
474#121—614no—
475#121—1228no—
476#121—1222no—
477#121—1222no—
478#121—1228no—
479#121—1222no—
480#121C4×D6114yes—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—42no—
483C2×C4⋊C4—611no—
484C2×C4⋊C4—614no—
485C2×C4⋊C4—612no—
486C2×C4⋊C4—1222no—
487C2×C4⋊C4—1221no—
488C2×C4⋊C4—1221no—
489C2×C4⋊C4—2442no—
490C2×C4⋊C4C22×D6112yes—
491C2×C4⋊C4C22×D6111yescharacteristic
492C2×C22⋊C4—21no—
493C2×C22⋊C4—1228no—
494C2×C22⋊C4—1221no—
495C2×C22⋊C4—1221no—
496C2×C22⋊C4—1221no—
497C2×C22⋊C4—1222no—
498C2×C22⋊C4—1222no—
499C2×C22⋊C4—2444no—
500#102—42no—
501#102—2442no—
502#102—2442no—
503#102—2442no—
504C22⋊C8—22no—
505C22⋊C8—1224no—
506C22⋊C8—1222no—
507#95—1222no—
508#95—1222no—
509C24—21no—
510C24—611no—
511C24—611no—
512C24—614no—
513C24—1222no—
514C24—1222no—
515C24—1224no—
516C24—1222no—
517C24—1222no—
518C24—1221no—
519C24—2441no—
520C24—2441no—
521C24—2442no—
522C24—2442no—
523C24—2442no—
524C24—2442no—
525C24—2442no—
526C24—2442no—
527C24D4×D6111yescharacteristic
528C2×D4—24no—
529C2×D4—21no—
530C2×D4—22no—
531C2×D4—22no—
532C2×D4—42no—
533C2×D4—42no—
534C2×D4—612no—
535C2×D4—1224no—
536C2×D4—1224no—
537C2×D4—1224no—
538C2×D4—1224no—
539C2×D4—1221no—
540C2×D4—1222no—
541C2×D4—1222no—
542C2×D4—2442no—
543C2×D4—2442no—
544C2×D4—2448no—
545C2×D4—2448no—
546C2×D4—2442no—
547C2×D4—2442no—
548C2×D4—24432no—
549C2×D4—2442no—
550C2×D4—2442no—
551C2×D4—2442no—
552C2×D4—2442no—
553C2×D4C2×C4×D6112yes—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—21no—
557C22×C4—22no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—611no—
562C22×C4—611no—
563C22×C4—614no—
564C22×C4—612no—
565C22×C4—612no—
566C22×C4—612no—
567C22×C4—612no—
568C22×C4—614no—
569C22×C4—614no—
570C22×C4—1224no—
571C22×C4—1222no—
572C22×C4—1222no—
573C22×C4—1222no—
574C22×C4—1222no—
575C22×C4—1221no—
576C22×C4—1222no—
577C22×C4—2448no—
578C22×C4—2448no—
579C22×C4—2441no—
580C22×C4—2441no—
581C22×C4—2441no—
582C22×C4—2441no—
583C22×C4—2442no—
584C22×C4—2442no—
585C22×C4—2441no—
586C22×C4—2441no—
587C22×C4—2442no—
588C22×C4—2442no—
589C22×C4—2442no—
590C22×C4C2×C4×D6112yes—
591C22×C4D4×D6112yes—
592C22×C4D4×D6111yescharacteristic
593C22×C4C23×D6111yescharacteristic
594M16—2448no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—22no—
598C2×C8—1222no—
599C2×C8—1222no—
600C2×C8—1222no—
601C4⋊C4—21no—
602C4⋊C4—22no—
603C4⋊C4—22no—
604C4⋊C4—42no—
605C4⋊C4—612no—
606C4⋊C4—1224no—
607C4⋊C4—1221no—
608C4⋊C4—1222no—
609C4⋊C4—1222no—
610C4⋊C4—2442no—
611C4⋊C4C2×C4×D6112yes—
612C22⋊C4—24no—
613C22⋊C4—1224no—
614C22⋊C4—1224no—
615C22⋊C4—1224no—
616C22⋊C4—2444no—
617C22⋊C4—2444no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—22no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—612no—
630C23—612no—
631C23—612no—
632C23—612no—
633C23—1228no—
634C23—1221no—
635C23—1221no—
636C23—1221no—
637C23—1221no—
638C23—1228no—
639C23—1221no—
640C23—1221no—
641C23—1221no—
642C23—1221no—
643C23—1221no—
644C23—1221no—
645C23—1222no—
646C23—4884no—
647C23—4884no—
648C23—4884no—
649C23—4884no—
650C23—2444no—
651C23—2444no—
652C23—2444no—
653C23—2444no—
654C23—2444no—
655C23—2448no—
656C23—2448no—
657C23—2448no—
658C23—2441no—
659C23—2441no—
660C23—2441no—
661C23—2441no—
662C23—2441no—
663C23—2441no—
664C23C22⋊C4×D6112yes—
665C23#1451980112yes—
666C23#1451980412yes—
667C23C2×D4×D6111yescharacteristic
668D4—24no—
669D4—48no—
670D4—42no—
671D4—1224no—
672D4—2448no—
673D4—2448no—
674D4—2448no—
675D4—2448no—
676D4—2442no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—22no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—84no—
688C2×C4—612no—
689C2×C4—612no—
690C2×C4—1221no—
691C2×C4—1221no—
692C2×C4—1221no—
693C2×C4—1221no—
694C2×C4—1224no—
695C2×C4—1224no—
696C2×C4—1224no—
697C2×C4—1224no—
698C2×C4—1222no—
699C2×C4—4884no—
700C2×C4—2444no—
701C2×C4—2444no—
702C2×C4—2448no—
703C2×C4—2444no—
704C2×C4—2442no—
705C2×C4—2442no—
706C2×C4—2442no—
707C2×C4—2441no—
708C2×C4—2441no—
709C2×C4C22⋊C4×D6112yes—
710C2×C4C22×C4×D6111yescharacteristic
711C2×C4C2×D4×D6111yescharacteristic
712C2×C4#1451982212yes—
713C2×C4#1451982312yes—
714C8—42no—
715C8—2442no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—81no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22—614no—
730C22—1222no—
731C22—1222no—
732C22—1222no—
733C22—1222no—
734C22—1222no—
735C22—1222no—
736C22—1222no—
737C22—1222no—
738C22—1222no—
739C22—48816no—
740C22—4881no—
741C22—4881no—
742C22—4881no—
743C22—4881no—
744C22—24416no—
745C22—2442no—
746C22—2442no—
747C22—2442no—
748C22—2441no—
749C22—2441no—
750C22—2441no—
751C22—2441no—
752C22#1683976514yes—
753C22C2×C22⋊C4×D6111yescharacteristic
754C22#1684032211yescharacteristic
755C22#1684032311yescharacteristic
756C22AGL(1,ℤ/8)×D6111yescharacteristic
757C22C2×#1451980111yescharacteristic
758C22C2×#1451980411yescharacteristic
759C22#137×D6111yescharacteristic
760C4—22no—
761C4—42no—
762C4—82no—
763C4—1222no—
764C4—1222no—
765C4—4882no—
766C4—2442no—
767C4#1684023412yes—
768C4#1684032012yes—
769C2—24no—
770C2—82no—
771C2—1224no—
772C2—4882no—
773C2—2442no—
774C2#2144839311yescharacteristic
775C2C2×#1683976511yescharacteristic
776C2#417×D6111yescharacteristic
777C2#2145661711yescharacteristic
778C2#2145661811yescharacteristic
779C2#2145662311yescharacteristic
780C2#2145662711yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1874C2
socleC23×C61C22×D4
prime radicalC2×#121×D61C2
cosocleC22×C4×C61C24
hypercenter#1874D61
hypocenterC61#21764
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1874

Complements

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

NH ≅ G/Ntype
2. C2×#16839724C2semidirect
3. C2×#16839619C2semidirect
4. #21446256C2semidirect
5. #21446254C2semidirect
6. #21446137C2semidirect
7. #21446136C2semidirect
8. #21446134C2semidirect
9. #21445908C2semidirect
10. #21445748C2semidirect
11. C61×#1874C2semidirect
15. C22×#11758189C22semidirect
22. #121×D61C4semidirect
23. C22×C4⋊Dic61C22semidirect
27. C2×#14519699C22semidirect
28. C2×#14519698C22semidirect
29. C2×#14519697C22semidirect
31. C2×C22⋊#92418C22semidirect
36. #16839619C22semidirect
38. #16839525C22semidirect
39. #16839524C22semidirect
40. #16839524C22semidirect
42. C22×C4⋊C4×C61C22semidirect
43. C2×#102×C61C22semidirect
44. C2×C22⋊C8×C61C22semidirect
45. C61×#340C22semidirect
59. C2×D4×D61C2×C4semidirect
76. #14519752C2×C4semidirect
82. #14519748C2×C4semidirect
89. C4⋊C4×D61C2×C4semidirect
387. #1874D61semidirect
416. C22×C4⋊C4C2×D61semidirect
422. C2×#102C2×D61semidirect
426. C2×C22⋊C8C2×D61semidirect
435. #340C2×D61semidirect
436. C61#21764semidirect

Maximal subgroups

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

subgroupindex
C2×#121×D612
C2×#168397242
C2×#168396192
#214462562
#214462542
#214461372
#214461362
#214461342
#214459082
#214457482
C61×#18742
#2176461