Finite Group Databasebeta

← #29681257

Subgroups — #29681257

Order 15616.

2278 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#121×D61C211yesmaximal, characteristic
2C22×#14519735C211yesmaximal, characteristic, complemented
3C2×#16839765C212yesmaximal, complemented
4C2×#16839724C211yesmaximal, characteristic, complemented
5#21446140C212yesmaximal, complemented
6#21446138C212yesmaximal, complemented
7#21446137C211yesmaximal, characteristic, complemented
8#21446136C211yesmaximal, characteristic, complemented
9#21446134C211yesmaximal, characteristic, complemented
10#21445537C212yesmaximal, complemented
11C61×#1874C211yesmaximal, characteristic, complemented
12C22×D4×D61—21no—
13C22×D4×D61C2211yescharacteristic
14C23×C4×D61C2211yescharacteristic
15C22×#11758189C2212yes—
16C2×#14519752C2211yescharacteristic
17C2×#14519751C2211yescharacteristic
18C2×#14519750—21no—
19C2×#14519749—21no—
20C2×#14519748C2211yescharacteristic
21#121×D61—24no—
22#121×D61C418yescomplemented
23C2×#14519735—28no—
24C2×#14519735—21no—
25C2×#14519735—21no—
26C2×#14519735C2212yes—
27C2×#14519735C2212yescomplemented
28C22×C4⋊Dic61C2211yescharacteristic, complemented
29C2×C4⋊C4×D61C2211yescharacteristic
30C22×#11758198—21no—
31C2×C22⋊C4×D61—21no—
32C22×C4×Dic61—21no—
33#16839765—28no—
34C2×#14519699C2212yescomplemented
35C2×#14519698C2212yescomplemented
36C2×#14519697C2212yescomplemented
37#16839724—24no—
38C2×C22⋊#92418C2211yescharacteristic, complemented
39C2×#14519689C2212yescomplemented
40#16839525C2212yescomplemented
41#16839524C2212yescomplemented
42#16839524C2212yescomplemented
43C2×#121×C61C2211yescharacteristic
44C22×C4⋊C4×C61C2211yescharacteristic, complemented
45C2×#102×C61C2212yescomplemented
46C2×C22⋊C8×C61C2211yescharacteristic, complemented
47C61×#340C2212yescomplemented
48C24×D61—21no—
49C24×D61D411yescharacteristic
50C22×D244—21no—
51C22×D244C2311yescharacteristic
52C22×C22⋊D61—21no—
53C22×C22⋊D61—21no—
54C22×C22⋊D61—21no—
55C2×D4×D61—28no—
56C2×D4×D61—24no—
57C2×D4×D61—22no—
58C2×D4×D61—24no—
59C2×D4×D61—44no—
60C2×D4×D61—44no—
61C2×D4×D61C2×C414yescomplemented
62C23×Dic61—21no—
63C23×Dic61D411yescharacteristic
64C22×C4×D61—24no—
65C22×C4×D61—24no—
66C22×C4×D61—21no—
67C22×C4×D61C2×C414yes—
68C22×C4×D61D411yescharacteristic
69C22×C4×D61D411yescharacteristic
70C22×C4×D61D414yes—
71C22×C4×D61C2311yescharacteristic
72C22×C4×D61C2311yescharacteristic
73C2×#11758189—24no—
74C2×#11758189—24no—
75C2×#11758189—24no—
76C22×#92418C2312yes—
77#14519752—22no—
78#14519752C2×C414yescomplemented
79#14519751—22no—
80#14519751C2×C414yes—
81#14519750—28no—
82#14519749—28no—
83#14519748—22no—
84#14519748C2×C414yescomplemented
85#14519735—28no—
86#14519735—28no—
87#14519735—24no—
88#14519735—24no—
89#14519735—24no—
90#14519735D418yescomplemented
91C2×C4⋊Dic61—21no—
92C2×C4⋊Dic61—24no—
93C2×C4⋊Dic61C2311yescharacteristic
94C2×C4⋊Dic61C2312yes—
95C2×#11758196—21no—
96C4⋊C4×D61—22no—
97C4⋊C4×D61C2×C414yescomplemented
98C2×C22⋊Dic61—21no—
99C2×#11758198—28no—
100C2×#11758198—22no—
101C2×#11758198—22no—
102C2×#11758198—21no—
103C2×#11758198—21no—
104C22⋊C4×D61—28no—
105C2×C4×Dic61—28no—
106C2×C4×Dic61—22no—
107C2×C4×Dic61—22no—
108#14519699—24no—
109#14519698—24no—
110#14519697—24no—
111C22⋊#92418—22no—
112#14519689—24no—
113C22×D4×C61—21no—
114C22×D4×C61C2311yescharacteristic
115C23×C4×C61—21no—
116C23×C4×C61C2311yescharacteristic
117C22×C8×C61C2312yes—
118#121×C61—22no—
119#121×C61C2×C414yes—
120C2×C4⋊C4×C61—21no—
121C2×C4⋊C4×C61—24no—
122C2×C4⋊C4×C61C2311yescharacteristic
123C2×C4⋊C4×C61C2312yes—
124C2×C22⋊C4×C61—21no—
125#102×C61—24no—
126C22⋊C8×C61—22no—
127C24×C61—21no—
128C24×C61C2×D411yescharacteristic
129C23×D61—22no—
130C23×D61—22no—
131C23×D61—22no—
132C23×D61—22no—
133C23×D61—21no—
134C23×D61—24no—
135C23×D61—41no—
136C23×D61—41no—
137C23×D61—42no—
138C23×D61—42no—
139C23×D61—42no—
140C23×D61—42no—
141C23×D61—42no—
142C23×D61—42no—
143C23×D61C22⋊C414yes—
144C23×D61C2×D411yescharacteristic
145C23×D61C2×D411yescharacteristic
146C2×D4×C61—24no—
147C2×D4×C61—22no—
148C2×D4×C61—21no—
149C2×D4×C61—22no—
150C2×D4×C61—42no—
151C2×D4×C61—42no—
152C2×D4×C61C22×C412yes—
153C22×C4×C61—22no—
154C22×C4×C61—22no—
155C22×C4×C61—24no—
156C22×C4×C61—21no—
157C22×C4×C61—22no—
158C22×C4×C61—42no—
159C22×C4×C61—42no—
160C22×C4×C61C22×C412yes—
161C22×C4×C61C2×D411yescharacteristic
162C22×C4×C61C2×D412yes—
163C22×C4×C61C2411yescharacteristic
164C2×C22⋊D61—24no—
165C2×C22⋊D61—24no—
166C2×C22⋊D61—24no—
167C2×C22⋊D61—42no—
168C2×C22⋊D61—42no—
169C2×C22⋊D61—42no—
170C2×C22⋊D61—42no—
171C2×C22⋊D61—42no—
172C2×C22⋊D61—42no—
173C22×Dic61—22no—
174C22×Dic61—22no—
175C22×Dic61—24no—
176C22×Dic61—21no—
177C22×Dic61—22no—
178C22×Dic61—42no—
179C22×Dic61—42no—
180C22×Dic61C22⋊C414yes—
181C22×Dic61C2×D411yescharacteristic
182C22×Dic61C2×D411yescharacteristic
183D4×D61—216no—
184D4×D61—432no—
185D4×D61—48no—
186C2×D244—22no—
187C2×D244—22no—
188C2×D244—24no—
189C2×D244—21no—
190C2×D244—42no—
191C2×D244—42no—
192C2×D244C22×C412yes—
193C2×C4×D61—22no—
194C2×C4×D61—22no—
195C2×C4×D61—22no—
196C2×C4×D61—22no—
197C2×C4×D61—22no—
198C2×C4×D61—22no—
199C2×C4×D61—216no—
200C2×C4×D61—216no—
201C2×C4×D61—24no—
202C2×C4×D61—42no—
203C2×C4×D61—42no—
204C2×C4×D61C22⋊C414yes—
205C2×C4×D61C22⋊C414yes—
206C2×C4×D61C22×C412yes—
207C2×C4×D61C22×C412yes—
208C2×C4×D61C2×D412yes—
209C2×C4×D61C2×D414yes—
210C2×C4×D61C2×D412yes—
211C2×C4×D61#4114yes—
212C2×C8×C61—22no—
213C2×C8×C61—22no—
214C2×C8×C61—22no—
215C4⋊C4×C61—24no—
216C4⋊C4×C61—22no—
217C4⋊C4×C61—21no—
218C4⋊C4×C61C22×C412yes—
219C4⋊C4×C61C2×D414yescomplemented
220C22⋊C4×C61—24no—
221C22⋊Dic61—24no—
222#11758198—28no—
223#11758198—28no—
224#11758198—24no—
225#11758198—24no—
226C4⋊Dic61—24no—
227C4⋊Dic61—21no—
228C4⋊Dic61—22no—
229C4⋊Dic61C22×C412yes—
230C4⋊Dic61C2×D414yescomplemented
231#11758196—24no—
232C4×Dic61—28no—
233C4×Dic61—28no—
234C2×#92418—22no—
235C2×#92418—22no—
236C2×#92418—22no—
237#11758189—48no—
238C23×C61—21no—
239C23×C61—21no—
240C23×C61—21no—
241C23×C61—21no—
242C23×C61—22no—
243C23×C61—41no—
244C23×C61—41no—
245C23×C61—41no—
246C23×C61—41no—
247C23×C61—41no—
248C23×C61—41no—
249C23×C61C2×C22⋊C412yes—
250C23×C61AGL(1,ℤ/8)12yes—
251C23×C61AGL(1,ℤ/8)12yes—
252C23×C61C22×D411yescharacteristic
253C22×D61—21no—
254C22×D61—21no—
255C22×D61—21no—
256C22×D61—21no—
257C22×D61—21no—
258C22×D61—21no—
259C22×D61—21no—
260C22×D61—21no—
261C22×D61—21no—
262C22×D61—21no—
263C22×D61—28no—
264C22×D61—28no—
265C22×D61—22no—
266C22×D61—44no—
267C22×D61—44no—
268C22×D61—44no—
269C22×D61—44no—
270C22×D61—44no—
271C22×D61—48no—
272C22×D61—48no—
273C22×D61—41no—
274C22×D61—41no—
275C22×D61—41no—
276C22×D61—41no—
277C22×D61—41no—
278C22×D61—41no—
279C22×D61—48no—
280C22×D61—84no—
281C22×D61—84no—
282C22×D61—84no—
283C22×D61—84no—
284C22×D61C2×C22⋊C412yes—
285C22×D61C2×C22⋊C412yes—
286C22×D61#12012yes—
287C22×D61#12312yes—
288D4×C61—24no—
289D4×C61—48no—
290D4×C61—42no—
291C2×C4×C61—21no—
292C2×C4×C61—21no—
293C2×C4×C61—24no—
294C2×C4×C61—24no—
295C2×C4×C61—22no—
296C2×C4×C61—24no—
297C2×C4×C61—48no—
298C2×C4×C61—41no—
299C2×C4×C61—41no—
300C2×C4×C61—42no—
301C2×C4×C61—42no—
302C2×C4×C61C2×C22⋊C412yes—
303C2×C4×C61C23×C411yescharacteristic
304C2×C4×C61C22×D412yes—
305C2×C4×C61C22×D411yescharacteristic
306C2×C4×C61C2×#4112yes—
307C22⋊D61—48no—
308C22⋊D61—48no—
309C22⋊D61—48no—
310C2×Dic61—21no—
311C2×Dic61—21no—
312C2×Dic61—28no—
313C2×Dic61—22no—
314C2×Dic61—24no—
315C2×Dic61—48no—
316C2×Dic61—41no—
317C2×Dic61—41no—
318C2×Dic61—42no—
319C2×Dic61—42no—
320C2×Dic61C2×C22⋊C412yes—
321C2×Dic61C2×C22⋊C412yes—
322C2×Dic61#12012yes—
323C2×Dic61#12312yes—
324D244—24no—
325D244—48no—
326D244—42no—
327C4×D61—28no—
328C4×D61—24no—
329C4×D61—24no—
330C4×D61—28no—
331C4×D61—48no—
332C4×D61C4×D418yes—
333C4×D61#12118yes—
334C8×C61—42no—
335#92418—42no—
336#20912—611nomaximal, Sylow
337C22×C61—22no—
338C22×C61—22no—
339C22×C61—22no—
340C22×C61—22no—
341C22×C61—22no—
342C22×C61—22no—
343C22×C61—42no—
344C22×C61—42no—
345C22×C61—42no—
346C22×C61—81no—
347C22×C61—81no—
348C22×C61—81no—
349C22×C61—81no—
350C22×C61#41814yescomplemented
351C22×C61C22×C22⋊C411yescharacteristic
352C22×C61C2×#12011yescharacteristic
353C22×C61C2×#12311yescharacteristic
354C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
355C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
356C22×C61#57511yescharacteristic
357C22×C61#57511yescharacteristic
358C2×D61—22no—
359C2×D61—22no—
360C2×D61—22no—
361C2×D61—22no—
362C2×D61—22no—
363C2×D61—22no—
364C2×D61—22no—
365C2×D61—22no—
366C2×D61—22no—
367C2×D61—416no—
368C2×D61—41no—
369C2×D61—41no—
370C2×D61—41no—
371C2×D61—41no—
372C2×D61—42no—
373C2×D61—42no—
374C2×D61—42no—
375C2×D61—816no—
376C2×D61—81no—
377C2×D61—81no—
378C2×D61—81no—
379C2×D61—81no—
380C2×D61#38614yes—
381C4×C61—22no—
382C4×C61—42no—
383C4×C61—44no—
384C4×C61C2×C4×D412yes—
385C4×C61C2×#12112yes—
386Dic61—22no—
387Dic61—42no—
388Dic61—44no—
389Dic61#38614yes—
390C22×#121—611no—
391C22×#117—611no—
392C2×#418—612no—
393C2×#407—611no—
394#1875—612no—
395#1875—612no—
396#1874—611no—
397#1874—611no—
398#1874—611no—
399#1874D6111yescharacteristic, complemented
400#1736—612no—
401C2×C61—24no—
402C2×C61—82no—
403C2×C61C2×#38611yescharacteristic
404C2×C61C2×#41811yescharacteristic
405C2×C61#289611yescharacteristic
406C2×C61#300611yescharacteristic
407C2×C61#300611yescharacteristic
408C2×C61#309411yescharacteristic
409C2×C61#309411yescharacteristic
410D61—24no—
411D61—42no—
412D61—82no—
413C23×D4—611no—
414C23×D4—1221no—
415C24×C4—611no—
416C22×M16—612no—
417C2×#121—611no—
418C2×#121—611no—
419C2×#121—618no—
420C2×#121—611no—
421C2×#121—1221no—
422C2×#121—1224no—
423C2×#121—1221no—
424C2×#121C2×D6111yescharacteristic
425C2×#117—612no—
426C2×#117—612no—
427C2×#117—1228no—
428C2×#117—1221no—
429C2×#117—1221no—
430C22×C4⋊C4—611no—
431C22×C4⋊C4—611no—
432C22×C4⋊C4C2×D6111yescharacteristic, complemented
433C22×C22⋊C4—1221no—
434C22×C22⋊C4—1221no—
435C22×C42—1221no—
436#418—1228no—
437C2×#102—612no—
438C2×#102—612no—
439C2×#102—612no—
440C2×#102C2×D6112yescomplemented
441#407—1224no—
442C2×C22⋊C8—611no—
443C2×C22⋊C8—612no—
444C2×C22⋊C8C2×D6111yescharacteristic, complemented
445#340—612no—
446#340—612no—
447#340—612no—
448#340C2×D6112yescomplemented
449C61#2091211yescharacteristic, complemented, Sylow
450C25—611no—
451C25—1221no—
452C22×D4—21no—
453C22×D4—614no—
454C22×D4—611no—
455C22×D4—1221no—
456C22×D4—1224no—
457C22×D4—1224no—
458C22×D4—1222no—
459C22×D4—1221no—
460C22×D4—1228no—
461C22×D4—1221no—
462C22×D4—1221no—
463C22×D4—2444no—
464C22×D4—2444no—
465C22×D4C22×D6111yescharacteristic
466C23×C4—21no—
467C23×C4—611no—
468C23×C4—611no—
469C23×C4—614no—
470C23×C4—611no—
471C23×C4—611no—
472C23×C4—614no—
473C23×C4—611no—
474C23×C4—1224no—
475C23×C4—1224no—
476C23×C4—1221no—
477C23×C4—1221no—
478C23×C4C22×D6111yescharacteristic
479C2×M16—1224no—
480C2×M16—1224no—
481C2×M16—1224no—
482C22×C8—612no—
483C22×C8C22×D6112yes—
484#121—22no—
485#121—614no—
486#121—614no—
487#121—614no—
488#121—1228no—
489#121—1222no—
490#121—1222no—
491#121—1228no—
492#121—1222no—
493#121C4×D6114yes—
494#117—618no—
495#117—1224no—
496#117—1224no—
497#117—1228no—
498#117—1228no—
499#117—1224no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—24no—
502C2×C4⋊C4—612no—
503C2×C4⋊C4—611no—
504C2×C4⋊C4—614no—
505C2×C4⋊C4—1222no—
506C2×C4⋊C4—1224no—
507C2×C4⋊C4—1221no—
508C2×C4⋊C4—1221no—
509C2×C4⋊C4C22×D6111yescharacteristic
510C2×C4⋊C4C22×D6112yes—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—1228no—
513C2×C22⋊C4—1221no—
514C2×C22⋊C4—1222no—
515C2×C22⋊C4—1222no—
516C2×C22⋊C4—1228no—
517C2×C22⋊C4—1221no—
518C2×C22⋊C4—1221no—
519C2×C42—1222no—
520C2×C42—1222no—
521C2×C42—1228no—
522#102—24no—
523#102—1224no—
524#102—1224no—
525#102—1224no—
526C22⋊C8—22no—
527C22⋊C8—1224no—
528C22⋊C8—1222no—
529C24—21no—
530C24—611no—
531C24—611no—
532C24—614no—
533C24—1222no—
534C24—1222no—
535C24—1224no—
536C24—1222no—
537C24—1222no—
538C24—1221no—
539C24—2441no—
540C24—2441no—
541C24—2442no—
542C24—2442no—
543C24—2442no—
544C24—2442no—
545C24—2442no—
546C24—2442no—
547C24D4×D6111yescharacteristic
548C2×D4—24no—
549C2×D4—22no—
550C2×D4—21no—
551C2×D4—22no—
552C2×D4—42no—
553C2×D4—42no—
554C2×D4—612no—
555C2×D4—1224no—
556C2×D4—12216no—
557C2×D4—1224no—
558C2×D4—1224no—
559C2×D4—1224no—
560C2×D4—1222no—
561C2×D4—1221no—
562C2×D4—1222no—
563C2×D4—2442no—
564C2×D4—2442no—
565C2×D4—2448no—
566C2×D4—2442no—
567C2×D4—2442no—
568C2×D4—24432no—
569C2×D4—2442no—
570C2×D4—2442no—
571C2×D4—2442no—
572C2×D4—2442no—
573C2×D4C2×C4×D6112yes—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—24no—
577C22×C4—22no—
578C22×C4—21no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—611no—
582C22×C4—612no—
583C22×C4—612no—
584C22×C4—614no—
585C22×C4—614no—
586C22×C4—611no—
587C22×C4—614no—
588C22×C4—612no—
589C22×C4—612no—
590C22×C4—614no—
591C22×C4—614no—
592C22×C4—1222no—
593C22×C4—1222no—
594C22×C4—12216no—
595C22×C4—12216no—
596C22×C4—1222no—
597C22×C4—1222no—
598C22×C4—1224no—
599C22×C4—1222no—
600C22×C4—1222no—
601C22×C4—1222no—
602C22×C4—1222no—
603C22×C4—1224no—
604C22×C4—1222no—
605C22×C4—1221no—
606C22×C4—2442no—
607C22×C4—2442no—
608C22×C4—2442no—
609C22×C4—2442no—
610C22×C4C2×C4×D6112yes—
611C22×C4D4×D6112yes—
612C22×C4D4×D6111yescharacteristic
613C22×C4C23×D6111yescharacteristic
614M16—2448no—
615C2×C8—22no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—1222no—
619C2×C8—1222no—
620C2×C8—1222no—
621C4⋊C4—24no—
622C4⋊C4—22no—
623C4⋊C4—21no—
624C4⋊C4—612no—
625C4⋊C4—614no—
626C4⋊C4—1224no—
627C4⋊C4—1224no—
628C4⋊C4—1222no—
629C4⋊C4—1221no—
630C4⋊C4C2×C4×D6112yes—
631C4⋊C4D4×D6114yescomplemented
632C22⋊C4—24no—
633C22⋊C4—1224no—
634C22⋊C4—1228no—
635C22⋊C4—1228no—
636C22⋊C4—1224no—
637C22⋊C4—1224no—
638C42—1228no—
639C42—1228no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—22no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—612no—
652C23—612no—
653C23—612no—
654C23—612no—
655C23—1228no—
656C23—1221no—
657C23—1221no—
658C23—1221no—
659C23—1221no—
660C23—1221no—
661C23—1221no—
662C23—1228no—
663C23—1221no—
664C23—1221no—
665C23—1221no—
666C23—1221no—
667C23—1222no—
668C23—4884no—
669C23—4884no—
670C23—4884no—
671C23—4884no—
672C23—2444no—
673C23—2444no—
674C23—2444no—
675C23—2444no—
676C23—2444no—
677C23—2448no—
678C23—2448no—
679C23—2448no—
680C23—2441no—
681C23—2441no—
682C23—2441no—
683C23—2441no—
684C23—2441no—
685C23—2441no—
686C23C22⋊C4×D6112yes—
687C23#1451980112yes—
688C23#1451980412yes—
689C23C2×D4×D6111yescharacteristic
690D4—24no—
691D4—48no—
692D4—42no—
693D4—1224no—
694D4—2448no—
695D4—2448no—
696D4—2448no—
697D4—2448no—
698D4—2442no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—48no—
706C2×C4—42no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—42no—
710C2×C4—612no—
711C2×C4—612no—
712C2×C4—612no—
713C2×C4—618no—
714C2×C4—618no—
715C2×C4—612no—
716C2×C4—1228no—
717C2×C4—1228no—
718C2×C4—1228no—
719C2×C4—1221no—
720C2×C4—1221no—
721C2×C4—1224no—
722C2×C4—1224no—
723C2×C4—1222no—
724C2×C4—1224no—
725C2×C4—2448no—
726C2×C4—2448no—
727C2×C4—2441no—
728C2×C4—2442no—
729C2×C4—2441no—
730C2×C4—2442no—
731C2×C4C22⋊C4×D6112yes—
732C2×C4C22×C4×D6111yescharacteristic
733C2×C4C2×D4×D6112yes—
734C2×C4C2×D4×D6111yescharacteristic
735C2×C4#41×D6112yes—
736C8—42no—
737C8—2442no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—614no—
752C22—1222no—
753C22—1222no—
754C22—1222no—
755C22—1222no—
756C22—1222no—
757C22—1222no—
758C22—1222no—
759C22—1222no—
760C22—1222no—
761C22—48816no—
762C22—4881no—
763C22—4881no—
764C22—4881no—
765C22—4881no—
766C22—24416no—
767C22—2442no—
768C22—2442no—
769C22—2442no—
770C22—2441no—
771C22—2441no—
772C22—2441no—
773C22—2441no—
774C22#1683976514yescomplemented
775C22C2×C22⋊C4×D6111yescharacteristic
776C22#120×D6111yescharacteristic
777C22#123×D6111yescharacteristic
778C22C2×#1451980111yescharacteristic
779C22C2×#1451980411yescharacteristic
780C22#1684055811yescharacteristic
781C22#1684056111yescharacteristic
782C4—22no—
783C4—44no—
784C4—42no—
785C4—614no—
786C4—1222no—
787C4—2444no—
788C4—2442no—
789C4C4×D4×D6112yes—
790C4#121×D6112yes—
791C2—24no—
792C2—82no—
793C2—1224no—
794C2—4882no—
795C2—2442no—
796C2#386×D6111yescharacteristic
797C2C2×#1683976511yescharacteristic
798C2#2145433511yescharacteristic
799C2#2145506611yescharacteristic
800C2#2145507011yescharacteristic
801C2#2145575411yescharacteristic
802C2#2145575611yescharacteristic
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#20912
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. C22×#14519735C2semidirect
3. C2×#16839765C2semidirect
4. C2×#16839724C2semidirect
5. #21446140C2semidirect
6. #21446138C2semidirect
7. #21446137C2semidirect
8. #21446136C2semidirect
9. #21446134C2semidirect
10. #21445537C2semidirect
11. C61×#1874C2semidirect
22. #121×D61C4semidirect
27. C2×#14519735C22semidirect
28. C22×C4⋊Dic61C22semidirect
34. C2×#14519699C22semidirect
35. C2×#14519698C22semidirect
36. C2×#14519697C22semidirect
38. C2×C22⋊#92418C22semidirect
39. C2×#14519689C22semidirect
40. #16839525C22semidirect
41. #16839524C22semidirect
42. #16839524C22semidirect
44. C22×C4⋊C4×C61C22semidirect
45. C2×#102×C61C22semidirect
46. C2×C22⋊C8×C61C22semidirect
47. C61×#340C22semidirect
61. C2×D4×D61C2×C4semidirect
78. #14519752C2×C4semidirect
84. #14519748C2×C4semidirect
90. #14519735D4semidirect
97. C4⋊C4×D61C2×C4semidirect
219. C4⋊C4×C61C2×D4semidirect
230. C4⋊Dic61C2×D4semidirect
350. C22×C61#418semidirect
399. #1874D61semidirect
432. C22×C4⋊C4C2×D61semidirect
440. C2×#102C2×D61semidirect
444. C2×C22⋊C8C2×D61semidirect
448. #340C2×D61semidirect
449. C61#20912semidirect
631. C4⋊C4D4×D61semidirect
774. C22#16839765semidirect

Maximal subgroups

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

subgroupindex
C2×#121×D612
C22×#145197352
C2×#168397652
C2×#168397242
#214461402
#214461382
#214461372
#214461362
#214461342
#214455372
C61×#18742
#2091261