Finite Group Databasebeta

← #29681236

Subgroups — #29681236

Order 15616.

2258 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840275C211yesmaximal, characteristic
2C22×C4⋊C4×D61C211yesmaximal, characteristic, complemented
3C2×#16839762C212yesmaximal, complemented
4C2×#16839724C211yesmaximal, characteristic, complemented
5#21446136C211yesmaximal, characteristic, complemented
6#21446135C212yesmaximal, complemented
7#21446134C211yesmaximal, characteristic, complemented
8#21446127C211yesmaximal, characteristic, complemented
9#21446123C212yesmaximal, complemented
10#21445537C212yesmaximal, complemented
11C61×#1872C211yesmaximal, characteristic, complemented
12C22×#11758226C2211yescharacteristic
13C23×C4×D61—21no—
14C23×C4×D61C2211yescharacteristic
15C22×#11758189C2212yes—
16#16840275—24no—
17#16840275C418yescomplemented
18C2×#14519762—21no—
19C2×#14519753C2211yescharacteristic
20C2×#14519752C2211yescharacteristic
21C2×#14519751C2211yescharacteristic
22C2×#14519747—21no—
23C2×#14519739—21no—
24C2×#14519737—21no—
25C2×#14519735C2211yescharacteristic
26C22×C4⋊Dic61C2211yescharacteristic
27C22×#11758196—21no—
28C2×C4⋊C4×D61—28no—
29C2×C4⋊C4×D61—21no—
30C2×C4⋊C4×D61—21no—
31C2×C4⋊C4×D61C2212yes—
32C2×C4⋊C4×D61C2212yes—
33#16839762—28no—
34C2×#14519701C2212yescomplemented
35C2×#14519699C2212yescomplemented
36C2×#14519697C2212yescomplemented
37#16839724—24no—
38C2×C22⋊#92418C2211yescharacteristic
39C2×#14519689C2212yes—
40#16839525C2212yescomplemented
41#16839524C2212yescomplemented
42#16839524C2212yescomplemented
43C2×C22⋊Q8×C61C2211yescharacteristic
44C22×C4⋊C4×C61C2211yescharacteristic
45C2×#103×C61C2212yescomplemented
46C2×C22⋊C8×C61C2211yescharacteristic
47C61×#340C2212yescomplemented
48C24×D61D411yescharacteristic
49C2×#11758226—22no—
50C2×#11758226—24no—
51C2×#11758226—24no—
52C2×#11758226C2×C414yescomplemented
53C22×D244—21no—
54C22×D244—21no—
55C22×D244C2311yescharacteristic
56C22×C22⋊D61—21no—
57C23×Dic61—21no—
58C23×Dic61D411yescharacteristic
59C22×C4×D61—24no—
60C22×C4×D61—24no—
61C22×C4×D61—28no—
62C22×C4×D61—22no—
63C22×C4×D61—22no—
64C22×C4×D61—21no—
65C22×C4×D61—44no—
66C22×C4×D61—44no—
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#14519762—28no—
78#14519753—22no—
79#14519753C2×C414yescomplemented
80#14519752—22no—
81#14519752C2×C414yescomplemented
82#14519751—22no—
83#14519751C2×C414yescomplemented
84#14519747—28no—
85#14519739—28no—
86#14519737—28no—
87#14519735—22no—
88#14519735C2×C414yescomplemented
89C2×C4⋊Dic61—21no—
90C2×C4⋊Dic61—24no—
91C2×C4⋊Dic61C2311yescharacteristic
92C2×C4⋊Dic61C2312yes—
93C2×#11758196—28no—
94C2×#11758196—22no—
95C2×#11758196—22no—
96C2×#11758196—21no—
97C4⋊C4×D61—28no—
98C4⋊C4×D61—28no—
99C4⋊C4×D61—24no—
100C4⋊C4×D61—24no—
101C4⋊C4×D61—24no—
102C4⋊C4×D61D418yescomplemented
103C2×#11758198—21no—
104C2×#11758198—21no—
105C2×#11758198—21no—
106C2×#11758198—21no—
107C2×C4×Dic61—21no—
108#14519701—24no—
109#14519699—24no—
110#14519697—24no—
111C22⋊#92418—22no—
112#14519689—24no—
113C22×Q8×C61C2311yescharacteristic
114C23×C4×C61—21no—
115C23×C4×C61C2311yescharacteristic
116C22×C8×C61C2312yes—
117C22⋊Q8×C61—22no—
118C22⋊Q8×C61C2×C414yescomplemented
119C2×C4⋊C4×C61—21no—
120C2×C4⋊C4×C61—21no—
121C2×C4⋊C4×C61—24no—
122C2×C4⋊C4×C61C2311yescharacteristic
123C2×C4⋊C4×C61C2312yes—
124C2×C22⋊C4×C61—21no—
125#103×C61—24no—
126C22⋊C8×C61—22no—
127C24×C61C2×D411yescharacteristic
128C23×D61—22no—
129C23×D61—22no—
130C23×D61—22no—
131C23×D61—22no—
132C23×D61—22no—
133C23×D61—22no—
134C23×D61—21no—
135C23×D61C22⋊C414yes—
136C23×D61C2×D411yescharacteristic
137C23×D61C2×D411yescharacteristic
138C2×Q8×C61—21no—
139C2×Q8×C61—22no—
140C2×Q8×C61—22no—
141C2×Q8×C61C22×C412yescomplemented
142C22×C4×C61—22no—
143C22×C4×C61—22no—
144C22×C4×C61—24no—
145C22×C4×C61—22no—
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C22×C4×C61—42no—
149C22×C4×C61—42no—
150C22×C4×C61C22×C412yes—
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2×D412yes—
153C22×C4×C61C2411yescharacteristic
154C2×C22⋊D61—24no—
155C2×C22⋊D61—42no—
156C2×C22⋊D61—42no—
157C22×Dic61—22no—
158C22×Dic61—22no—
159C22×Dic61—24no—
160C22×Dic61—22no—
161C22×Dic61—21no—
162C22×Dic61—42no—
163C22×Dic61—42no—
164C22×Dic61C22⋊C414yes—
165C22×Dic61C2×D411yescharacteristic
166C22×Dic61C2×D411yescharacteristic
167#11758226—216no—
168#11758226—48no—
169C2×D244—22no—
170C2×D244—22no—
171C2×D244—24no—
172C2×D244—24no—
173C2×D244—21no—
174C2×D244—42no—
175C2×D244—42no—
176C2×D244—42no—
177C2×D244—42no—
178C2×D244C22×C412yescomplemented
179C2×C4×D61—22no—
180C2×C4×D61—22no—
181C2×C4×D61—22no—
182C2×C4×D61—22no—
183C2×C4×D61—22no—
184C2×C4×D61—22no—
185C2×C4×D61—216no—
186C2×C4×D61—216no—
187C2×C4×D61—28no—
188C2×C4×D61—28no—
189C2×C4×D61—24no—
190C2×C4×D61—432no—
191C2×C4×D61—44no—
192C2×C4×D61—44no—
193C2×C4×D61—44no—
194C2×C4×D61—44no—
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×D414yes—
203C2×C4×D61C2×D412yes—
204C2×C4×D61#4114yes—
205C2×C8×C61—22no—
206C2×C8×C61—22no—
207C2×C8×C61—22no—
208C4⋊C4×C61—24no—
209C4⋊C4×C61—24no—
210C4⋊C4×C61—22no—
211C4⋊C4×C61—21no—
212C4⋊C4×C61C22×C412yescomplemented
213C4⋊C4×C61C2×D414yes—
214C22⋊C4×C61—24no—
215#11758198—24no—
216#11758198—24no—
217#11758198—24no—
218#11758198—24no—
219C4⋊Dic61—24no—
220C4⋊Dic61—22no—
221C4⋊Dic61—21no—
222C4⋊Dic61C22×C412yescomplemented
223C4⋊Dic61C2×D414yes—
224#11758196—28no—
225#11758196—24no—
226#11758196—28no—
227C4×Dic61—24no—
228C2×#92418—22no—
229C2×#92418—22no—
230C2×#92418—22no—
231#11758189—48no—
232C23×C61—21no—
233C23×C61—21no—
234C23×C61—21no—
235C23×C61—21no—
236C23×C61C2×C22⋊C412yes—
237C23×C61AGL(1,ℤ/8)12yes—
238C23×C61#13712yes—
239C23×C61C22×D411yescharacteristic
240C22×D61—28no—
241C22×D61—28no—
242C22×D61—28no—
243C22×D61—28no—
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—28no—
255C22×D61—22no—
256C22×D61—41no—
257C22×D61—41no—
258C22×D61—41no—
259C22×D61—41no—
260C22×D61—41no—
261C22×D61—41no—
262C22×D61C2×C22⋊C412yes—
263C22×D61C2×C22⋊C412yes—
264C22×D61#12012yes—
265C22×D61#12312yes—
266C22×D61AGL(1,ℤ/8)12yes—
267C22×D61#13712yes—
268Q8×C61—24no—
269Q8×C61—42no—
270C2×C4×C61—21no—
271C2×C4×C61—21no—
272C2×C4×C61—24no—
273C2×C4×C61—24no—
274C2×C4×C61—22no—
275C2×C4×C61—22no—
276C2×C4×C61—24no—
277C2×C4×C61—48no—
278C2×C4×C61—41no—
279C2×C4×C61—41no—
280C2×C4×C61—42no—
281C2×C4×C61—42no—
282C2×C4×C61—41no—
283C2×C4×C61—41no—
284C2×C4×C61C2×C22⋊C412yes—
285C2×C4×C61C23×C411yescharacteristic
286C2×C4×C61C22×D412yes—
287C2×C4×C61C22×D411yescharacteristic
288C2×C4×C61C2×#4112yes—
289C22⋊D61—48no—
290C2×Dic61—21no—
291C2×Dic61—21no—
292C2×Dic61—28no—
293C2×Dic61—22no—
294C2×Dic61—24no—
295C2×Dic61—48no—
296C2×Dic61—42no—
297C2×Dic61—42no—
298C2×Dic61—41no—
299C2×Dic61—41no—
300C2×Dic61C2×C22⋊C412yes—
301C2×Dic61C2×C22⋊C412yes—
302C2×Dic61#12012yes—
303C2×Dic61#12312yes—
304D244—24no—
305D244—48no—
306D244—48no—
307D244—42no—
308C4×D61—28no—
309C4×D61—24no—
310C4×D61—24no—
311C4×D61—28no—
312C4×D61—416no—
313C4×D61—416no—
314C4×D61—48no—
315C4×D61C4×D418yes—
316C4×D61#12118yes—
317C8×C61—42no—
318#92418—42no—
319#20909—611nomaximal, Sylow
320C22×C61—22no—
321C22×C61—22no—
322C22×C61—22no—
323C22×C61—22no—
324C22×C61—22no—
325C22×C61—22no—
326C22×C61#41714yescomplemented
327C22×C61C22×C22⋊C411yescharacteristic
328C22×C61C2×#12011yescharacteristic
329C22×C61C2×#12311yescharacteristic
330C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
331C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
332C22×C61C2×#13711yescharacteristic
333C22×C61C2×#13711yescharacteristic
334C2×D61—232no—
335C2×D61—22no—
336C2×D61—22no—
337C2×D61—22no—
338C2×D61—22no—
339C2×D61—22no—
340C2×D61—22no—
341C2×D61—22no—
342C2×D61—22no—
343C2×D61—22no—
344C2×D61—22no—
345C2×D61—22no—
346C2×D61—22no—
347C2×D61—42no—
348C2×D61—42no—
349C2×D61—42no—
350C2×D61—81no—
351C2×D61—81no—
352C2×D61—81no—
353C2×D61—81no—
354C2×D61#38614yes—
355C2×D61#41714yescomplemented
356C4×C61—22no—
357C4×C61—42no—
358C4×C61—44no—
359C4×C61—42no—
360C4×C61C2×C4×D412yes—
361C4×C61C2×#12112yes—
362Dic61—22no—
363Dic61—42no—
364Dic61—44no—
365Dic61#38614yes—
366C2×#525—611no—
367C23×C4⋊C4—611no—
368C2×#417—612no—
369C2×#407—611no—
370#1874—611no—
371#1874—612no—
372#1874—611no—
373#1872—612no—
374#1872—611no—
375#1872D6111yescharacteristic, complemented
376#1736—612no—
377C2×C61—24no—
378C2×C61C2×#38611yescharacteristic
379C2×C61C2×#41711yescharacteristic
380C2×C61C2×#41711yescharacteristic
381C2×C61#300311yescharacteristic
382C2×C61#300411yescharacteristic
383C2×C61#309211yescharacteristic
384C2×C61#309211yescharacteristic
385D61—24no—
386D61—24no—
387D61—82no—
388C22×#41—611no—
389C24×C4—611no—
390C24×C4—1221no—
391C22×M16—612no—
392#525—618no—
393#525—1224no—
394C2×#123—1221no—
395C2×C22⋊Q8—611no—
396C2×C22⋊Q8C2×D6111yescharacteristic
397C2×#121—611no—
398C2×#121—611no—
399C2×#120—1221no—
400C2×C4×D4—1221no—
401C2×C4×D4—1221no—
402C2×#117—611no—
403C22×C4⋊C4—612no—
404C22×C4⋊C4—611no—
405C22×C4⋊C4—612no—
406C22×C4⋊C4—1228no—
407C22×C4⋊C4—1221no—
408C22×C4⋊C4—1221no—
409C22×C4⋊C4—1221no—
410C22×C4⋊C4C2×D6111yescharacteristic
411#417—1228no—
412C2×#103—612no—
413C2×#103C2×D6112yescomplemented
414C2×#102—612no—
415C2×#102—612no—
416#407—1224no—
417C2×C22⋊C8—611no—
418C2×C22⋊C8—612no—
419C2×C22⋊C8C2×D6111yescharacteristic
420#340—612no—
421#340—612no—
422#340—612no—
423#340C2×D6112yescomplemented
424C61#2090911yescharacteristic, complemented, Sylow
425C25—611no—
426C2×#41—614no—
427C2×#41—1222no—
428C2×#41—1224no—
429C2×#41—1224no—
430C22×Q8C22×D6111yescharacteristic
431C22×D4—611no—
432C22×D4—1221no—
433C22×D4—1221no—
434C22×D4—1221no—
435C23×C4—21no—
436C23×C4—611no—
437C23×C4—611no—
438C23×C4—614no—
439C23×C4—611no—
440C23×C4—611no—
441C23×C4—614no—
442C23×C4—611no—
443C23×C4—1224no—
444C23×C4—1224no—
445C23×C4—1221no—
446C23×C4—1222no—
447C23×C4—1222no—
448C23×C4—1228no—
449C23×C4—1221no—
450C23×C4—2444no—
451C23×C4—2444no—
452C23×C4C22×D6111yescharacteristic
453C2×M16—1224no—
454C2×M16—1224no—
455C2×M16—1224no—
456C22×C8—612no—
457C22×C8C22×D6112yes—
458#123—1228no—
459C22⋊Q8—22no—
460C22⋊Q8—614no—
461C22⋊Q8—1222no—
462C22⋊Q8C4×D6114yescomplemented
463#121—614no—
464#121—614no—
465#121—1222no—
466#121—1222no—
467#120—1228no—
468C4×D4—1228no—
469C4×D4—1228no—
470#117—614no—
471#117—1222no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—24no—
475C2×C4⋊C4—612no—
476C2×C4⋊C4—611no—
477C2×C4⋊C4—618no—
478C2×C4⋊C4—1224no—
479C2×C4⋊C4—1224no—
480C2×C4⋊C4—1228no—
481C2×C4⋊C4—1228no—
482C2×C4⋊C4—1224no—
483C2×C4⋊C4—1222no—
484C2×C4⋊C4—1222no—
485C2×C4⋊C4—1221no—
486C2×C4⋊C4—1228no—
487C2×C4⋊C4—1221no—
488C2×C4⋊C4—1224no—
489C2×C4⋊C4C22×D6111yescharacteristic
490C2×C4⋊C4C22×D6112yes—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—1221no—
493C2×C22⋊C4—1221no—
494C2×C22⋊C4—1221no—
495C2×C22⋊C4—1221no—
496C2×C42—1221no—
497#103—24no—
498#103—1224no—
499#102—1224no—
500#102—1224no—
501C22⋊C8—22no—
502C22⋊C8—1224no—
503C22⋊C8—1222no—
504C24—611no—
505C24—611no—
506C24—614no—
507C24—1222no—
508C24—1222no—
509C24—1222no—
510C24—1222no—
511C24—1222no—
512C24—1222no—
513C24—1221no—
514C24D4×D6111yescharacteristic
515#41—12216no—
516#41—2448no—
517C2×Q8—21no—
518C2×Q8—22no—
519C2×Q8—22no—
520C2×Q8C2×C4×D6112yescomplemented
521C2×D4—612no—
522C2×D4—1224no—
523C2×D4—1224no—
524C2×D4—1224no—
525C2×D4—1222no—
526C2×D4—1221no—
527C2×D4—1222no—
528C2×D4—2442no—
529C2×D4—2442no—
530C2×D4—2442no—
531C2×D4—2442no—
532C2×D4—2442no—
533C2×D4—2442no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—24no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—611no—
543C22×C4—612no—
544C22×C4—614no—
545C22×C4—612no—
546C22×C4—614no—
547C22×C4—611no—
548C22×C4—614no—
549C22×C4—612no—
550C22×C4—612no—
551C22×C4—614no—
552C22×C4—614no—
553C22×C4—1222no—
554C22×C4—1222no—
555C22×C4—12216no—
556C22×C4—12216no—
557C22×C4—1224no—
558C22×C4—1222no—
559C22×C4—1222no—
560C22×C4—1228no—
561C22×C4—1228no—
562C22×C4—1222no—
563C22×C4—1222no—
564C22×C4—1222no—
565C22×C4—1222no—
566C22×C4—1224no—
567C22×C4—1221no—
568C22×C4—1222no—
569C22×C4—2442no—
570C22×C4—2442no—
571C22×C4—2444no—
572C22×C4—24432no—
573C22×C4—2444no—
574C22×C4—2444no—
575C22×C4—2444no—
576C22×C4—2442no—
577C22×C4—2442no—
578C22×C4C2×C4×D6112yes—
579C22×C4D4×D6112yes—
580C22×C4D4×D6111yescharacteristic
581C22×C4C23×D6111yescharacteristic
582M16—2448no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—1222no—
587C2×C8—1222no—
588C2×C8—1222no—
589C4⋊C4—24no—
590C4⋊C4—22no—
591C4⋊C4—21no—
592C4⋊C4—24no—
593C4⋊C4—612no—
594C4⋊C4—614no—
595C4⋊C4—1228no—
596C4⋊C4—1224no—
597C4⋊C4—1228no—
598C4⋊C4—1224no—
599C4⋊C4—1222no—
600C4⋊C4—1221no—
601C4⋊C4C2×C4×D6112yescomplemented
602C4⋊C4D4×D6114yes—
603C22⋊C4—24no—
604C22⋊C4—1224no—
605C22⋊C4—1224no—
606C22⋊C4—1224no—
607C22⋊C4—1224no—
608C42—1224no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—612no—
614C23—612no—
615C23—612no—
616C23—612no—
617C23—612no—
618C23—612no—
619C23—1228no—
620C23—1228no—
621C23—1228no—
622C23—1228no—
623C23—1228no—
624C23—1228no—
625C23—1221no—
626C23—1221no—
627C23—1228no—
628C23—1221no—
629C23—1221no—
630C23—1221no—
631C23—1221no—
632C23—1221no—
633C23—1221no—
634C23—1222no—
635C23—2441no—
636C23—2441no—
637C23—2441no—
638C23—2441no—
639C23—2441no—
640C23—2441no—
641C23C22⋊C4×D6112yes—
642C23#1451980412yes—
643C23#1451980912yes—
644C23C2×D4×D6111yescharacteristic
645Q8—24no—
646Q8—42no—
647D4—1224no—
648D4—2448no—
649D4—2448no—
650D4—2448no—
651D4—2442no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—24no—
655C2×C4—24no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—24no—
659C2×C4—48no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—42no—
663C2×C4—41no—
664C2×C4—42no—
665C2×C4—41no—
666C2×C4—612no—
667C2×C4—612no—
668C2×C4—612no—
669C2×C4—618no—
670C2×C4—618no—
671C2×C4—612no—
672C2×C4—1228no—
673C2×C4—1228no—
674C2×C4—1228no—
675C2×C4—1221no—
676C2×C4—1221no—
677C2×C4—1224no—
678C2×C4—1224no—
679C2×C4—1222no—
680C2×C4—1224no—
681C2×C4—2448no—
682C2×C4—24416no—
683C2×C4—24416no—
684C2×C4—2448no—
685C2×C4—2442no—
686C2×C4—2442no—
687C2×C4—2441no—
688C2×C4—2441no—
689C2×C4C22⋊C4×D6112yes—
690C2×C4C22×C4×D6111yescharacteristic
691C2×C4C2×D4×D6112yes—
692C2×C4C2×D4×D6111yescharacteristic
693C2×C4#41×D6112yes—
694C8—42no—
695C8—2442no—
696C22—22no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—614no—
703C22—614no—
704C22—12232no—
705C22—1222no—
706C22—1222no—
707C22—1222no—
708C22—1222no—
709C22—1222no—
710C22—1222no—
711C22—1222no—
712C22—1222no—
713C22—1222no—
714C22—1222no—
715C22—1222no—
716C22—1222no—
717C22—4881no—
718C22—4881no—
719C22—4881no—
720C22—4881no—
721C22—2442no—
722C22—2442no—
723C22—2442no—
724C22#1683976214yescomplemented
725C22C2×C22⋊C4×D6111yescharacteristic
726C22#120×D6111yescharacteristic
727C22#123×D6111yescharacteristic
728C22AGL(1,ℤ/8)×D6111yescharacteristic
729C22C2×#1451980411yescharacteristic
730C22#137×D6111yescharacteristic
731C22C2×#1451980911yescharacteristic
732C4—22no—
733C4—42no—
734C4—44no—
735C4—42no—
736C4—614no—
737C4—1222no—
738C4—2444no—
739C4—2442no—
740C4C4×D4×D6112yes—
741C4#121×D6112yes—
742C2—24no—
743C2—1224no—
744C2—1224no—
745C2—4882no—
746C2#386×D6111yescharacteristic
747C2#417×D6111yescharacteristic
748C2C2×#1683976211yescharacteristic
749C2#2145504711yescharacteristic
750C2#2145505411yescharacteristic
751C2#2145574311yescharacteristic
752C2#2145574611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1872C2
socleC23×C61C22×D4
prime radicalC2×#16840275C2
cosocleC22×C4×C61C24
hypercenter#1872D61
hypocenterC61#20909
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1872

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊C4×D61C2semidirect
3. C2×#16839762C2semidirect
4. C2×#16839724C2semidirect
5. #21446136C2semidirect
6. #21446135C2semidirect
7. #21446134C2semidirect
8. #21446127C2semidirect
9. #21446123C2semidirect
10. #21445537C2semidirect
11. C61×#1872C2semidirect
17. #16840275C4semidirect
34. C2×#14519701C22semidirect
35. C2×#14519699C22semidirect
36. C2×#14519697C22semidirect
40. #16839525C22semidirect
41. #16839524C22semidirect
42. #16839524C22semidirect
45. C2×#103×C61C22semidirect
47. C61×#340C22semidirect
52. C2×#11758226C2×C4semidirect
79. #14519753C2×C4semidirect
81. #14519752C2×C4semidirect
83. #14519751C2×C4semidirect
88. #14519735C2×C4semidirect
102. C4⋊C4×D61D4semidirect
118. C22⋊Q8×C61C2×C4semidirect
141. C2×Q8×C61C22×C4semidirect
178. C2×D244C22×C4semidirect
212. C4⋊C4×C61C22×C4semidirect
222. C4⋊Dic61C22×C4semidirect
326. C22×C61#417semidirect
355. C2×D61#417semidirect
375. #1872D61semidirect
413. C2×#103C2×D61semidirect
423. #340C2×D61semidirect
424. C61#20909semidirect
462. C22⋊Q8C4×D61semidirect
520. C2×Q8C2×C4×D61semidirect
601. C4⋊C4C2×C4×D61semidirect
724. C22#16839762semidirect

Maximal subgroups

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

subgroupindex
C2×#168402752
C22×C4⋊C4×D612
C2×#168397622
C2×#168397242
#214461362
#214461352
#214461342
#214461272
#214461232
#214455372
C61×#18722
#2090961