Finite Group Databasebeta

← #29707525

Subgroups — #29707525

Order 15616.

1650 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840273C211yesmaximal, characteristic
2C2×#16839804C211yesmaximal, characteristic, complemented
3C2×#16839764C211yesmaximal, characteristic, complemented
4C2×#16839764C211yesmaximal, characteristic, complemented
5C2×#16839622C211yesmaximal, characteristic, complemented
6#21447023C212yesmaximal, complemented
7#21447016C212yesmaximal, complemented
8#21447009C212yesmaximal, complemented
9#21447002C212yesmaximal, complemented
10#21445539C211yesmaximal, characteristic, complemented
11C2×C61×#407C211yesmaximal, characteristic, complemented
12C22×#11758222C2211yescharacteristic
13#16840273—24no—
14#16840273—24no—
15C2×#14519760—21no—
16C2×#14519756C2211yescharacteristic
17C2×#14519756C2211yescharacteristic
18C2×#14519751C2211yescharacteristic
19C2×#14519751C2211yescharacteristic
20C2×#14519746—21no—
21C2×C4×C22⋊D61—21no—
22C2×C4×C22⋊D61—21no—
23C2×#14519736C2211yescharacteristic
24C22×C4⋊Dic61C2211yescharacteristic
25C22×C4⋊Dic61C2211yescharacteristic
26C22×C22⋊Dic61—21no—
27#16839804—24no—
28C2×#14519711C2212yescomplemented
29C2×#14519709C2212yescomplemented
30#16839764—24no—
31#16839764—24no—
32C2×#14519702C2212yescomplemented
33C2×#14519702C2212yescomplemented
34C2×#14519699C2212yescomplemented
35C2×#14519699C2212yescomplemented
36#16839622—21no—
37#16839622—21no—
38#16839622C2212yes—
39#16839622C2212yes—
40C2×#14519684—21no—
41#16839525C2212yescomplemented
42#16839525C2212yescomplemented
43C24×C4×C61C2211yescharacteristic
44C22×M16×C61C2211yescharacteristic
45C22×M16×C61C2211yescharacteristic
46C61×#407—24no—
47C2×C22⋊C8×C61C2212yes—
48C2×C22⋊C8×C61C2212yes—
49C2×#11758222—22no—
50C2×#11758222—22no—
51C2×#11758222—22no—
52C2×#11758222—22no—
53C2×#11758222—22no—
54C2×#11758222D414yes—
55C22×Dic122C2311yescharacteristic
56C22×D244C2311yescharacteristic
57C22×C22⋊D61—21no—
58C22×C22⋊D61—21no—
59C22×C22⋊D61—21no—
60C23×Dic61—21no—
61C23×Dic61—21no—
62C22×C4×D61—21no—
63#14519760—28no—
64#14519756—22no—
65#14519756—22no—
66#14519756—22no—
67#14519756—22no—
68#14519751—22no—
69#14519751—22no—
70#14519751—22no—
71#14519751—22no—
72#14519746—28no—
73C4×C22⋊D61—28no—
74C4×C22⋊D61—28no—
75#14519736—22no—
76#14519736D414yes—
77C2×C4⋊Dic61—22no—
78C2×C4⋊Dic61—22no—
79C2×C4⋊Dic61—22no—
80C2×C4⋊Dic61—22no—
81C2×C4⋊Dic61—21no—
82C2×C4⋊Dic61—21no—
83C2×C4⋊Dic61C2312yes—
84C2×C4⋊Dic61C2312yes—
85C2×C4⋊Dic61C2311yescharacteristic
86C2×C4⋊Dic61C2311yescharacteristic
87C2×#11758196—21no—
88C2×#11758196—21no—
89C2×C22⋊Dic61—21no—
90C2×C22⋊Dic61—21no—
91C2×C22⋊Dic61—21no—
92C2×C22⋊Dic61—22no—
93C2×C22⋊Dic61—22no—
94C2×C22⋊Dic61—44no—
95C2×#11758198—21no—
96C2×#11758198—21no—
97C2×C4×Dic61—21no—
98#14519711—24no—
99#14519709—24no—
100#14519702—24no—
101#14519702—24no—
102#14519699—24no—
103#14519699—24no—
104#14519684—22no—
105#14519684—22no—
106C25×C61D411yescharacteristic
107C23×C4×C61—22no—
108C23×C4×C61—22no—
109C23×C4×C61—22no—
110C23×C4×C61—22no—
111C23×C4×C61—22no—
112C23×C4×C61—22no—
113C23×C4×C61D411yescharacteristic
114C23×C4×C61D411yescharacteristic
115C23×C4×C61D411yescharacteristic
116C23×C4×C61C2311yescharacteristic
117C23×C4×C61C2311yescharacteristic
118C23×C4×C61C2311yescharacteristic
119C2×M16×C61—22no—
120C2×M16×C61—22no—
121C2×M16×C61—22no—
122C2×M16×C61—22no—
123C2×M16×C61—22no—
124C2×M16×C61D414yescomplemented
125C22×C8×C61C2312yes—
126C22×C8×C61C2312yes—
127C22⋊C8×C61—24no—
128C22⋊C8×C61—24no—
129C24×C61—22no—
130C24×C61—22no—
131C24×C61—22no—
132C24×C61—22no—
133C24×C61—22no—
134C24×C61—41no—
135C24×C61—41no—
136C24×C61C2×D411yescharacteristic
137C24×C61C2×D411yescharacteristic
138C24×C61C2×D411yescharacteristic
139C23×D61—21no—
140C22×C4×C61—22no—
141C22×C4×C61—22no—
142C22×C4×C61—22no—
143C22×C4×C61—22no—
144C22×C4×C61—22no—
145C22×C4×C61—22no—
146C22×C4×C61—22no—
147C22×C4×C61—22no—
148C22×C4×C61—22no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—44no—
162C22×C4×C61—44no—
163C22×C4×C61—44no—
164C22×C4×C61—44no—
165C22×C4×C61C2×D411yescharacteristic
166C22×C4×C61C2×D411yescharacteristic
167C22×C4×C61C2×D411yescharacteristic
168C22×C4×C61C2×D412yes—
169C22×C4×C61C2×D412yes—
170C22×C4×C61C2×D412yes—
171C22×C4×C61#4112yes—
172C22×C4×C61#4112yes—
173C22×C4×C61#4112yes—
174C22×C4×C61C2411yescharacteristic
175C2×C22⋊D61—24no—
176C2×C22⋊D61—24no—
177C2×C22⋊D61—24no—
178C2×C22⋊D61—42no—
179C2×C22⋊D61—42no—
180C2×C22⋊D61—42no—
181C2×C22⋊D61—42no—
182C2×C22⋊D61—42no—
183C2×C22⋊D61—42no—
184C22×Dic61—21no—
185C22×Dic61—21no—
186C22×Dic61—21no—
187C22×Dic61—22no—
188C22×Dic61—22no—
189C22×Dic61—42no—
190C22×Dic61—42no—
191C22×Dic61—42no—
192C22×Dic61—42no—
193C22×Dic61—42no—
194C22×Dic61—42no—
195#11758222—28no—
196#11758222—28no—
197#11758222—44no—
198#11758222—44no—
199C2×D244—21no—
200C2×D244—21no—
201C2×D244—21no—
202C2×D244—21no—
203C2×D244—21no—
204C2×D244C2×D412yes—
205C2×C4×D61—24no—
206C2×C4×D61—42no—
207C2×C4×D61—42no—
208C2×Dic122—21no—
209C2×Dic122—21no—
210C2×Dic122—21no—
211C2×Dic122—21no—
212C2×Dic122—21no—
213C2×Dic122C2×D412yes—
214M16×C61—28no—
215M16×C61—44no—
216C2×C8×C61—22no—
217C2×C8×C61—22no—
218C2×C8×C61—22no—
219C2×C8×C61—22no—
220C2×C8×C61—22no—
221C2×C8×C61C2×D414yes—
222C22⋊Dic61—24no—
223C22⋊Dic61—24no—
224C22⋊Dic61—24no—
225C22⋊Dic61—44no—
226C22⋊Dic61—44no—
227#11758198—24no—
228#11758198—24no—
229C4⋊Dic61—21no—
230C4⋊Dic61—21no—
231C4⋊Dic61—22no—
232C4⋊Dic61—22no—
233C4⋊Dic61—22no—
234C4⋊Dic61—22no—
235C4⋊Dic61—42no—
236C4⋊Dic61—42no—
237C4⋊Dic61C2×D412yes—
238C4⋊Dic61C2×D412yes—
239#11758196—24no—
240#11758196—24no—
241C4×Dic61—24no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61—28no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—21no—
252C23×C61—21no—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61—21no—
256C23×C61—21no—
257C23×C61—21no—
258C23×C61—21no—
259C23×C61—44no—
260C23×C61—44no—
261C23×C61—44no—
262C23×C61—44no—
263C23×C61—44no—
264C23×C61—44no—
265C23×C61#12012yes—
266C23×C61#12112yes—
267C23×C61#12312yes—
268C23×C61AGL(1,ℤ/8)12yes—
269C23×C61#13712yes—
270C23×C61C22×D411yescharacteristic
271C22×D61—22no—
272C22×D61—41no—
273C22×D61—41no—
274C22×D61—41no—
275C22×D61—41no—
276C22×D61—41no—
277C22×D61—41no—
278C2×C4×C61—21no—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—21no—
283C2×C4×C61—21no—
284C2×C4×C61—44no—
285C2×C4×C61—41no—
286C2×C4×C61—41no—
287C2×C4×C61—41no—
288C2×C4×C61—41no—
289C2×C4×C61—41no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61—41no—
293C2×C4×C61—44no—
294C2×C4×C61—44no—
295C2×C4×C61#12012yes—
296C2×C4×C61#12114yes—
297C2×C4×C61#12114yes—
298C2×C4×C61#12112yes—
299C2×C4×C61#12314yes—
300C2×C4×C61#12312yes—
301C2×C4×C61#12414yes—
302C2×C4×C61C22×D411yescharacteristic
303C2×C4×C61C22×D411yescharacteristic
304C2×C4×C61C22×D411yescharacteristic
305C2×C4×C61C2×#4111yescharacteristic
306C2×C4×C61C2×#4111yescharacteristic
307C2×C4×C61C2×#4111yescharacteristic
308C22⋊D61—48no—
309C22⋊D61—48no—
310C22⋊D61—48no—
311C2×Dic61—22no—
312C2×Dic61—22no—
313C2×Dic61—22no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61—41no—
317C2×Dic61—41no—
318C2×Dic61—41no—
319C2×Dic61—41no—
320C2×Dic61—42no—
321C2×Dic61—42no—
322C2×Dic61—42no—
323C2×Dic61—42no—
324C2×Dic61—42no—
325C2×Dic61—42no—
326C2×Dic61—84no—
327C2×Dic61—84no—
328D244—22no—
329D244—22no—
330D244—41no—
331D244—41no—
332C4×D61—48no—
333Dic122—22no—
334Dic122—22no—
335Dic122—41no—
336Dic122—41no—
337C8×C61—24no—
338C8×C61—42no—
339#23482—611nomaximal, Sylow
340C22×C61—22no—
341C22×C61—22no—
342C22×C61—22no—
343C22×C61—22no—
344C22×C61—22no—
345C22×C61—22no—
346C22×C61—22no—
347C22×C61—22no—
348C22×C61—22no—
349C22×C61—22no—
350C22×C61—22no—
351C22×C61—22no—
352C22×C61—416no—
353C22×C61—41no—
354C22×C61—41no—
355C22×C61—41no—
356C22×C61—41no—
357C22×C61—41no—
358C22×C61—41no—
359C22×C61—41no—
360C22×C61—41no—
361C22×C61#39414yes—
362C22×C61C2×#12011yescharacteristic
363C22×C61C2×#12111yescharacteristic
364C22×C61C2×#12311yescharacteristic
365C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
366C22×C61C2×#13711yescharacteristic
367C22×C61#57511yescharacteristic
368C22×C61#57511yescharacteristic
369C2×D61—42no—
370C2×D61—42no—
371C2×D61—42no—
372C2×D61—81no—
373C2×D61—81no—
374C2×D61—81no—
375C2×D61—81no—
376C4×C61—41no—
377C4×C61—41no—
378C4×C61#39414yes—
379C4×C61C2×#12111yescharacteristic
380C4×C61C2×#12111yescharacteristic
381C4×C61C2×#12311yescharacteristic
382C4×C61C2×#12411yescharacteristic
383Dic61—42no—
384Dic61—42no—
385Dic61—42no—
386Dic61—82no—
387Dic61—82no—
388C2×#525—611no—
389C2×#428—611no—
390C2×#417—611no—
391C2×#417—611no—
392C2×#407D6111yescharacteristic, complemented
393C2×#380—611no—
394#2036—612no—
395#2035—612no—
396#2034—612no—
397#2033—612no—
398#1736—611no—
399C2×C61—24no—
400C2×C61—42no—
401C2×C61—42no—
402C2×C61C2×#39411yescharacteristic
403C2×C61#300611yescharacteristic
404C2×C61#300711yescharacteristic
405C2×C61#305511yescharacteristic
406C2×C61#305611yescharacteristic
407C2×C61#309211yescharacteristic
408C2×C61#309311yescharacteristic
409D61—82no—
410C22×#41—611no—
411C24×C4C2×D6111yescharacteristic
412C22×M16C2×D6111yescharacteristic
413C22×M16C2×D6111yescharacteristic
414#525—1224no—
415#525—1224no—
416C2×#123—1221no—
417C2×C22⋊Q8—611no—
418C2×C22⋊Q8—611no—
419C2×#121—611no—
420C2×#121—611no—
421C2×#120—1221no—
422C2×C4×D4—1221no—
423C2×C4×D4—1221no—
424C2×#117—611no—
425C22×C4⋊C4—611no—
426C22×C4⋊C4—611no—
427C22×C22⋊C4—1221no—
428#428—1224no—
429C2×#107—612no—
430C2×#106—612no—
431#417—1224no—
432#417—1224no—
433C2×#103—612no—
434C2×#103—612no—
435C2×#102—612no—
436C2×#102—612no—
437#407—24no—
438C2×C22⋊C8C2×D6112yes—
439C2×C22⋊C8C2×D6112yes—
440#380—612no—
441#380—612no—
442#380—1221no—
443#380—1221no—
444C2×#95—1221no—
445#340—612no—
446#340—612no—
447C61#2348211yescharacteristic, complemented, Sylow
448C25D24411yescharacteristic
449C2×#41—614no—
450C2×#41—1222no—
451C2×#41—1222no—
452C2×#41—1222no—
453C2×#41—1222no—
454C2×#41—1222no—
455C22×Q8—611no—
456C22×D4—611no—
457C22×D4—1221no—
458C22×D4—1221no—
459C22×D4—1221no—
460C23×C4—22no—
461C23×C4—22no—
462C23×C4—22no—
463C23×C4—22no—
464C23×C4—22no—
465C23×C4—22no—
466C23×C4—1221no—
467C23×C4—1221no—
468C23×C4—1221no—
469C23×C4D24411yescharacteristic
470C23×C4D24411yescharacteristic
471C23×C4D24411yescharacteristic
472C23×C4C22×D6111yescharacteristic
473C23×C4C22×D6111yescharacteristic
474C23×C4C22×D6111yescharacteristic
475C2×M16—22no—
476C2×M16—22no—
477C2×M16—22no—
478C2×M16—22no—
479C2×M16—22no—
480C2×M16C22⋊D6114yescomplemented
481C22×C8C22×D6112yes—
482C22×C8C22×D6112yes—
483#123—1228no—
484C22⋊Q8—1222no—
485C22⋊Q8—1222no—
486C22⋊Q8—1222no—
487C22⋊Q8—1222no—
488#121—1222no—
489#121—1222no—
490#121—1222no—
491#121—1222no—
492#120—1228no—
493C4×D4—1228no—
494C4×D4—1228no—
495#117—614no—
496#117—1222no—
497C2×C4⋊C4—611no—
498C2×C4⋊C4—611no—
499C2×C4⋊C4—612no—
500C2×C4⋊C4—612no—
501C2×C4⋊C4—1221no—
502C2×C4⋊C4—1221no—
503C2×C4⋊C4—1222no—
504C2×C4⋊C4—1222no—
505C2×C4⋊C4—1222no—
506C2×C4⋊C4—1222no—
507C2×C4⋊C4—1221no—
508C2×C4⋊C4—1221no—
509C2×C22⋊C4—1221no—
510C2×C22⋊C4—1221no—
511C2×C22⋊C4—1221no—
512C2×C22⋊C4—1221no—
513C2×C22⋊C4—1221no—
514C2×C22⋊C4—1222no—
515C2×C22⋊C4—1222no—
516C2×C22⋊C4—2444no—
517C2×C42—1221no—
518#107—1224no—
519#106—1224no—
520#103—1224no—
521#103—1224no—
522#102—1224no—
523#102—1224no—
524C22⋊C8—24no—
525C22⋊C8—24no—
526#95—1222no—
527#95—1222no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—41no—
534C24—41no—
535C24—1221no—
536C24C2×D24411yescharacteristic
537C24C2×D24411yescharacteristic
538C24C2×D24411yescharacteristic
539#41—1228no—
540#41—1228no—
541#41—2444no—
542#41—2444no—
543C2×Q8—612no—
544C2×Q8—1221no—
545C2×Q8—1221no—
546C2×Q8—1221no—
547C2×Q8—1221no—
548C2×Q8—1221no—
549C2×D4—612no—
550C2×D4—1224no—
551C2×D4—1224no—
552C2×D4—1224no—
553C2×D4—1221no—
554C2×D4—1221no—
555C2×D4—1221no—
556C2×D4—1221no—
557C2×D4—1221no—
558C2×D4—2442no—
559C2×D4—2442no—
560C2×D4—2442no—
561C2×D4—2442no—
562C2×D4—2442no—
563C2×D4—2442no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—1221no—
590C22×C4—1221no—
591C22×C4—1221no—
592C22×C4—1224no—
593C22×C4—1222no—
594C22×C4—1222no—
595C22×C4—2442no—
596C22×C4—2442no—
597C22×C4—2442no—
598C22×C4—2442no—
599C22×C4—2442no—
600C22×C4—2442no—
601C22×C4—2442no—
602C22×C4—2442no—
603C22×C4C2×D24411yescharacteristic
604C22×C4C2×D24411yescharacteristic
605C22×C4C2×D24411yescharacteristic
606C22×C4#1175822212yes—
607C22×C4D4×D6112yes—
608C22×C4D4×D6112yes—
609C22×C4#1175822412yes—
610C22×C4#1175822412yes—
611C22×C4C2×C22⋊D6112yes—
612C22×C4C23×D6111yescharacteristic
613M16—28no—
614M16—44no—
615C2×C8—22no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8C2×C22⋊D6114yes—
621C4⋊C4—612no—
622C4⋊C4—612no—
623C4⋊C4—1224no—
624C4⋊C4—1224no—
625C4⋊C4—1221no—
626C4⋊C4—1221no—
627C4⋊C4—1222no—
628C4⋊C4—1222no—
629C4⋊C4—1222no—
630C4⋊C4—1222no—
631C4⋊C4—2442no—
632C4⋊C4—2442no—
633C22⋊C4—1224no—
634C22⋊C4—1224no—
635C22⋊C4—1224no—
636C22⋊C4—1224no—
637C22⋊C4—1224no—
638C22⋊C4—2444no—
639C22⋊C4—2444no—
640C42—1224no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—28no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—44no—
659C23—44no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—1222no—
665C23—2441no—
666C23—2441no—
667C23—2441no—
668C23—2441no—
669C23—2441no—
670C23—2441no—
671C23#1451974712yes—
672C23#1451975112yes—
673C23#1451976112yes—
674C23#1451980512yes—
675C23#1451981012yes—
676C23C22×D24411yescharacteristic
677Q8—1222no—
678Q8—1222no—
679Q8—2441no—
680Q8—2441no—
681D4—1222no—
682D4—1222no—
683D4—2448no—
684D4—2448no—
685D4—2448no—
686D4—2441no—
687D4—2441no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—44no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—44no—
704C2×C4—44no—
705C2×C4—1222no—
706C2×C4—1222no—
707C2×C4—1222no—
708C2×C4—4884no—
709C2×C4—4884no—
710C2×C4—2442no—
711C2×C4—2442no—
712C2×C4—2442no—
713C2×C4—2442no—
714C2×C4—2442no—
715C2×C4—2442no—
716C2×C4—2441no—
717C2×C4—2441no—
718C2×C4—2441no—
719C2×C4—2441no—
720C2×C4—2441no—
721C2×C4—2441no—
722C2×C4—2448no—
723C2×C4#1451974712yes—
724C2×C4#1451974814yes—
725C2×C4#1451974914yes—
726C2×C4#1451975112yes—
727C2×C4#1451975914yes—
728C2×C4#1451976112yes—
729C2×C4#1451976314yes—
730C2×C4C2×D4×D6111yescharacteristic
731C2×C4C2×D4×D6111yescharacteristic
732C2×C4C22×C22⋊D6111yescharacteristic
733C2×C4C2×#1175822411yescharacteristic
734C2×C4C2×#1175822411yescharacteristic
735C2×C4C2×#1175822211yescharacteristic
736C8—24no—
737C8—42no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—416no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—4881no—
760C22—4881no—
761C22—4881no—
762C22—4881no—
763C22—2442no—
764C22—2442no—
765C22—2442no—
766C22#1683967814yes—
767C22C2×#1451974711yescharacteristic
768C22C2×#1451975111yescharacteristic
769C22C2×#1451976111yescharacteristic
770C22C2×#1451980511yescharacteristic
771C22C2×#1451981011yescharacteristic
772C22#1684056211yescharacteristic
773C22#1684056211yescharacteristic
774C4—41no—
775C4—41no—
776C4—4882no—
777C4—4882no—
778C4—2442no—
779C4—2442no—
780C4—2442no—
781C4#1683967814yes—
782C4C2×#1451974811yescharacteristic
783C4C2×#1451974911yescharacteristic
784C4C2×#1451975911yescharacteristic
785C4C2×#1451976311yescharacteristic
786C2—24no—
787C2—42no—
788C2—42no—
789C2—4882no—
790C2C2×#1683967811yescharacteristic
791C2#2145507311yescharacteristic
792C2#2145508111yescharacteristic
793C2#2145543811yescharacteristic
794C2#2145544911yescharacteristic
795C2#2145574411yescharacteristic
796C2#2145575211yescharacteristic
subgroupG/H
centerC23C22×D244
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#407C2
socleC23×C61C22×D4
prime radicalC2×#16840273C2
hypercenterC2×#407D61
hypocenterC61#23482
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
2. C2×#16839804C2semidirect
3. C2×#16839764C2semidirect
4. C2×#16839764C2semidirect
5. C2×#16839622C2semidirect
6. #21447023C2semidirect
7. #21447016C2semidirect
8. #21447009C2semidirect
9. #21447002C2semidirect
10. #21445539C2semidirect
11. C2×C61×#407C2semidirect
28. C2×#14519711C22semidirect
29. C2×#14519709C22semidirect
32. C2×#14519702C22semidirect
33. C2×#14519702C22semidirect
34. C2×#14519699C22semidirect
35. C2×#14519699C22semidirect
41. #16839525C22semidirect
42. #16839525C22semidirect
124. C2×M16×C61D4semidirect
392. C2×#407D61semidirect
447. C61#23482semidirect
480. C2×M16C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168402732
C2×#168398042
C2×#168397642
C2×#168396222
#214470232
#214470162
#214470092
#214470022
#214455392
C2×C61×#4072
#2348261