Finite Group Databasebeta

← #29603130

Subgroups — #29603130

Order 15616.

2474 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519761C211yesmaximal, characteristic
2C2×#16839641C211yesmaximal, characteristic
3C2×#16839639C211yesmaximal, characteristic
4C2×#16839637C211yesmaximal, characteristic, complemented
5C2×#16839623C211yesmaximal, characteristic, complemented
6C22×#14519684C211yesmaximal, characteristic, complemented
7#21444086C212yesmaximal, complemented
8#21444065C212yesmaximal, complemented
9#21444057C212yesmaximal, complemented
10#21444049C212yesmaximal, complemented
11C2×C4×C22⋊C4×C61C211yesmaximal, characteristic, complemented
12C23×C22⋊D61C2211yescharacteristic
13C24×Dic61C2211yescharacteristic
14C24×Dic61C2211yescharacteristic
15C2×#14519761—24no—
16C2×#14519761—24no—
17C2×#14519761C418yescomplemented
18C22×C4⋊Dic61C2212yes—
19C22×C4⋊Dic61C2212yes—
20C22×C22⋊Dic61C2211yescharacteristic
21C22×#11758198C2211yescharacteristic
22C22×#11758198C2212yes—
23C22×#11758198C2212yes—
24C22×#11758198C2211yescharacteristic
25#16839641—24no—
26#16839639—24no—
27#16839637—24no—
28#16839623—24no—
29C2×#14519684—24no—
30C2×#14519684C2212yes—
31C2×#14519684C2212yes—
32C2×#14519684C2212yes—
33C2×#14519684C2212yes—
34C2×#14519684C2211yescharacteristic
35C2×#14519684C2211yescharacteristic
36C2×#14519684C2212yes—
37C2×#14519684C2212yes—
38C24×C4×C61C2211yescharacteristic
39C22×C22⋊C4×C61C2211yescharacteristic
40C22×C22⋊C4×C61C2211yescharacteristic
41C22×C42×C61C2212yes—
42C4×C22⋊C4×C61—24no—
43C2×#95×C61C2212yes—
44C24×D61C2311yescharacteristic
45C22×C22⋊D61—22no—
46C22×C22⋊D61—22no—
47C22×C22⋊D61—22no—
48C22×C22⋊D61—22no—
49C22×C22⋊D61—22no—
50C22×C22⋊D61—22no—
51C22×C22⋊D61C2×C414yes—
52C23×Dic61—22no—
53C23×Dic61—22no—
54C23×Dic61—22no—
55C23×Dic61—22no—
56C23×Dic61—22no—
57C23×Dic61—22no—
58C23×Dic61—22no—
59C23×Dic61—24no—
60C23×Dic61—22no—
61C23×Dic61—22no—
62C23×Dic61—42no—
63C23×Dic61C2×C414yes—
64C23×Dic61C2311yescharacteristic
65C23×Dic61C2311yescharacteristic
66C23×Dic61C2312yes—
67C23×Dic61C2311yescharacteristic
68C23×Dic61C2312yes—
69#14519761—232no—
70C2×C4⋊Dic61—24no—
71C2×C4⋊Dic61—24no—
72C2×C4⋊Dic61—24no—
73C2×C4⋊Dic61—24no—
74C2×C4⋊Dic61—42no—
75C2×C4⋊Dic61C2×C418yescomplemented
76C2×C22⋊Dic61—22no—
77C2×C22⋊Dic61—22no—
78C2×C22⋊Dic61—22no—
79C2×#11758198—24no—
80C2×#11758198—24no—
81C2×#11758198—24no—
82C2×#11758198—22no—
83C2×#11758198—22no—
84C2×#11758198—24no—
85C2×#11758198—24no—
86C2×#11758198—42no—
87C2×#11758198—42no—
88C2×#11758198C2×C418yescomplemented
89#14519684—24no—
90#14519684—24no—
91#14519684—24no—
92#14519684—24no—
93#14519684—24no—
94#14519684—24no—
95#14519684—22no—
96#14519684—22no—
97C25×C61C2311yescharacteristic
98C23×C4×C61—22no—
99C23×C4×C61—22no—
100C23×C4×C61—24no—
101C23×C4×C61—42no—
102C23×C4×C61D414yes—
103C23×C4×C61C2311yescharacteristic
104C23×C4×C61C2312yes—
105C23×C4×C61C2312yes—
106C23×C4×C61C2311yescharacteristic
107C2×C22⋊C4×C61—22no—
108C2×C22⋊C4×C61—22no—
109C2×C22⋊C4×C61C2×C414yes—
110C2×C22⋊C4×C61D414yes—
111C2×C22⋊C4×C61D414yes—
112C2×C22⋊C4×C61D414yes—
113C2×C42×C61—24no—
114C2×C42×C61—24no—
115C2×C42×C61—42no—
116#95×C61—24no—
117C24×C61—22no—
118C24×C61—22no—
119C24×C61—22no—
120C24×C61—22no—
121C24×C61C22×C412yes—
122C24×C61C2×D412yes—
123C24×C61C2×D412yes—
124C24×C61C2×D412yes—
125C24×C61C2×D412yes—
126C24×C61#4112yes—
127C24×C61#4112yes—
128C24×C61C2411yescharacteristic
129C23×D61—21no—
130C23×D61—21no—
131C23×D61—21no—
132C23×D61—21no—
133C23×D61—21no—
134C23×D61—21no—
135C23×D61—22no—
136C23×D61—22no—
137C23×D61—22no—
138C23×D61—22no—
139C23×D61C22×C412yes—
140C22×C4×C61—21no—
141C22×C4×C61—22no—
142C22×C4×C61—21no—
143C22×C4×C61—22no—
144C22×C4×C61—22no—
145C22×C4×C61—22no—
146C22×C4×C61—22no—
147C22×C4×C61—28no—
148C22×C4×C61—21no—
149C22×C4×C61—22no—
150C22×C4×C61—22no—
151C22×C4×C61—22no—
152C22×C4×C61—21no—
153C22×C4×C61—22no—
154C22×C4×C61—22no—
155C22×C4×C61—22no—
156C22×C4×C61—22no—
157C22×C4×C61—22no—
158C22×C4×C61—28no—
159C22×C4×C61—44no—
160C22×C4×C61—48no—
161C22×C4×C61—48no—
162C22×C4×C61C22×C414yes—
163C22×C4×C61C2×D414yes—
164C22×C4×C61C2×D412yes—
165C22×C4×C61C2×D414yes—
166C22×C4×C61C2×D414yes—
167C22×C4×C61C2×D412yes—
168C22×C4×C61#4114yes—
169C2×C22⋊D61—28no—
170C2×C22⋊D61—28no—
171C2×C22⋊D61—28no—
172C2×C22⋊D61—44no—
173C2×C22⋊D61—44no—
174C2×C22⋊D61—44no—
175C2×C22⋊D61—44no—
176C22×Dic61—28no—
177C22×Dic61—28no—
178C22×Dic61—28no—
179C22×Dic61—28no—
180C22×Dic61—22no—
181C22×Dic61—22no—
182C22×Dic61—22no—
183C22×Dic61—22no—
184C22×Dic61—22no—
185C22×Dic61—22no—
186C22×Dic61—22no—
187C22×Dic61—21no—
188C22×Dic61—21no—
189C22×Dic61—21no—
190C22×Dic61—21no—
191C22×Dic61—22no—
192C22×Dic61—22no—
193C22×Dic61—22no—
194C22×Dic61—21no—
195C22×Dic61—21no—
196C22×Dic61—22no—
197C22×Dic61—22no—
198C22×Dic61—21no—
199C22×Dic61—21no—
200C22×Dic61—21no—
201C22×Dic61—21no—
202C22×Dic61—21no—
203C22×Dic61—21no—
204C22×Dic61—22no—
205C22×Dic61—22no—
206C22×Dic61—22no—
207C22×Dic61—22no—
208C22×Dic61—48no—
209C22×Dic61—48no—
210C22×Dic61—44no—
211C22×Dic61—44no—
212C22×Dic61—44no—
213C22×Dic61—44no—
214C22×Dic61—44no—
215C22×Dic61—44no—
216C22×Dic61C22×C414yes—
217C22×Dic61C22×C412yes—
218C22×Dic61#4114yes—
219C22⋊C4×C61—28no—
220C22⋊C4×C61C22⋊C4116yescomplemented
221C42×C61—48no—
222C22⋊Dic61—44no—
223#11758198—216no—
224#11758198—48no—
225#11758198—44no—
226#11758198—44no—
227C4⋊Dic61—216no—
228C4⋊Dic61—48no—
229C23×C61—24no—
230C23×C61—24no—
231C23×C61—22no—
232C23×C61—22no—
233C23×C61—24no—
234C23×C61—22no—
235C23×C61—22no—
236C23×C61—24no—
237C23×C61—24no—
238C23×C61—24no—
239C23×C61—24no—
240C23×C61—24no—
241C23×C61—24no—
242C23×C61—24no—
243C23×C61—24no—
244C23×C61—24no—
245C23×C61C2×C22⋊C414yes—
246C23×C61C4×D414yes—
247C23×C61C4×D414yes—
248C23×C61#12114yes—
249C23×C61#12114yes—
250C23×C61#12414yes—
251C23×C61#12714yes—
252C23×C61C23×C411yescharacteristic
253C23×C61C22×D411yescharacteristic
254C23×C61C22×D411yescharacteristic
255C23×C61C22×D411yescharacteristic
256C23×C61C22×D411yescharacteristic
257C23×C61C2×#4111yescharacteristic
258C23×C61C2×#4111yescharacteristic
259C23×C61C2×#4112yes—
260C23×C61C2×#4112yes—
261C23×C61H(5,𝔽2)12yes—
262C23×C612−1+412yes—
263C22×D61—22no—
264C22×D61—22no—
265C22×D61—22no—
266C22×D61—24no—
267C22×D61—24no—
268C22×D61—41no—
269C22×D61—41no—
270C22×D61—41no—
271C22×D61—41no—
272C22×D61—41no—
273C22×D61—42no—
274C22×D61—41no—
275C22×D61—41no—
276C22×D61—41no—
277C22×D61—42no—
278C22×D61—42no—
279C22×D61—42no—
280C22×D61—42no—
281C22×D61—42no—
282C22×D61—42no—
283C22×D61—42no—
284C22×D61—42no—
285C22×D61—42no—
286C2×C4×C61—24no—
287C2×C4×C61—24no—
288C2×C4×C61—22no—
289C2×C4×C61—22no—
290C2×C4×C61—24no—
291C2×C4×C61—24no—
292C2×C4×C61—24no—
293C2×C4×C61—24no—
294C2×C4×C61—24no—
295C2×C4×C61—24no—
296C2×C4×C61—24no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—24no—
301C2×C4×C61—24no—
302C2×C4×C61—416no—
303C2×C4×C61—42no—
304C2×C4×C61—42no—
305C2×C4×C61—42no—
306C2×C4×C61—42no—
307C2×C4×C61—42no—
308C2×C4×C61—42no—
309C2×C4×C61C2×C22⋊C418yes—
310C2×C4×C61#12314yescomplemented
311C22⋊D61—416no—
312C2×Dic61—22no—
313C2×Dic61—24no—
314C2×Dic61—24no—
315C2×Dic61—24no—
316C2×Dic61—22no—
317C2×Dic61—22no—
318C2×Dic61—24no—
319C2×Dic61—24no—
320C2×Dic61—24no—
321C2×Dic61—416no—
322C2×Dic61—42no—
323C2×Dic61—42no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—42no—
327C2×Dic61—41no—
328C2×Dic61—42no—
329C2×Dic61—42no—
330C2×Dic61—41no—
331C2×Dic61—42no—
332C2×Dic61—42no—
333C2×Dic61—42no—
334C2×Dic61—416no—
335C2×Dic61—41no—
336C2×Dic61—41no—
337C2×Dic61—41no—
338C2×Dic61—41no—
339C2×Dic61—41no—
340C2×Dic61—41no—
341C2×Dic61—42no—
342C2×Dic61—42no—
343C2×Dic61—42no—
344C2×Dic61—42no—
345#13996—611nomaximal, Sylow
346C22×C61—24no—
347C22×C61—28no—
348C22×C61—28no—
349C22×C61—24no—
350C22×C61—24no—
351C22×C61—28no—
352C22×C61—28no—
353C22×C61—24no—
354C22×C61—24no—
355C22×C61—24no—
356C22×C61#39018yes—
357C22×C61C22×C22⋊C411yescharacteristic
358C22×C61C2×C4×D411yescharacteristic
359C22×C61C2×C4×D411yescharacteristic
360C22×C61C4×#4112yes—
361C22×C61#52012yes—
362C22×C61C2×#12111yescharacteristic
363C22×C61C2×#12111yescharacteristic
364C22×C61C2×#12311yescharacteristic
365C22×C61#52511yescharacteristic
366C22×C61C2×#12411yescharacteristic
367C22×C61#52912yes—
368C22×C61C2×#12711yescharacteristic
369C22×C61#53411yescharacteristic
370C22×C61#53611yescharacteristic
371C22×C61#53912yes—
372C22×C61#54612yes—
373C22×C61#54612yes—
374C22×C61#54612yes—
375C22×C61#54712yes—
376C22×C61#54712yes—
377C22×C61#54712yes—
378C22×C61#55112yes—
379C22×C61#55212yes—
380C2×D61—42no—
381C2×D61—44no—
382C2×D61—44no—
383C2×D61—42no—
384C2×D61—42no—
385C2×D61—81no—
386C2×D61—81no—
387C2×D61—82no—
388C2×D61—82no—
389C2×D61—81no—
390C2×D61—81no—
391C4×C61—28no—
392C4×C61—24no—
393C4×C61—42no—
394C4×C61—44no—
395Dic61—44no—
396Dic61—44no—
397Dic61—42no—
398Dic61—81no—
399Dic61—81no—
400C22×#123—611no—
401C2×#386—611no—
402C2×#386—611no—
403C2×#385—611no—
404C2×#381—611no—
405C2×C4×C22⋊C4D6111yescharacteristic, complemented
406C22×#95—611no—
407#1445—612no—
408#1439—612no—
409#1437—612no—
410C4⋊#95—612no—
411C2×C61—28no—
412C2×C61C2×#39011yescharacteristic
413C2×C61C4×#12311yescharacteristic
414C2×C61#232211yescharacteristic
415C2×C61#233912yes—
416C2×C61#235912yes—
417C2×C61#241211yescharacteristic
418C2×C61#241311yescharacteristic
419C2×C61#242512yes—
420C2×C61#248812yes—
421C2×C61#250111yescharacteristic
422C2×C61#253911yescharacteristic
423D61—82no—
424C23×D4—611no—
425C24×C4—611no—
426C24×C4—611no—
427C24×C4C2×D6111yescharacteristic
428C2×#123—618no—
429C2×#123—1224no—
430C2×#123—1224no—
431C22×C4⋊C4—612no—
432C22×C4⋊C4—612no—
433C22×C22⋊C4—612no—
434C22×C22⋊C4—611no—
435C22×C22⋊C4—611no—
436C22×C22⋊C4—612no—
437C22×C22⋊C4—611no—
438C22×C22⋊C4C2×D6111yescharacteristic
439C22×C22⋊C4C2×D6111yescharacteristic
440C22×C42C2×D6112yes—
441#386—1224no—
442#386—1224no—
443#385—1224no—
444#381—1224no—
445C4×C22⋊C4—24no—
446C2×#95—611no—
447C2×#95—612no—
448C2×#95—612no—
449C2×#95—612no—
450C2×#95—612no—
451C2×#95—612no—
452C2×#95—612no—
453C2×#95—611no—
454C2×#95—1224no—
455C2×#95C2×D6112yes—
456C61#1399611yescharacteristic, complemented, Sylow
457C25—611no—
458C25C22×D6111yescharacteristic
459C22×D4—614no—
460C22×D4—1222no—
461C22×D4—1222no—
462C22×D4—1222no—
463C22×D4—1222no—
464C22×D4—1222no—
465C22×D4—1222no—
466C23×C4—22no—
467C23×C4—22no—
468C23×C4—24no—
469C23×C4—42no—
470C23×C4—614no—
471C23×C4—612no—
472C23×C4—612no—
473C23×C4—611no—
474C23×C4—611no—
475C23×C4—611no—
476C23×C4—1224no—
477C23×C4—1222no—
478C23×C4—1222no—
479C23×C4—1222no—
480C23×C4—1222no—
481C23×C4—1222no—
482C23×C4—1222no—
483C23×C4—1222no—
484C23×C4—1222no—
485C23×C4—1222no—
486C23×C4—2442no—
487C23×C4D24414yes—
488C23×C4C22×D6112yes—
489C23×C4C22×D6111yescharacteristic
490C23×C4C22×D6112yes—
491C23×C4C22×D6111yescharacteristic
492#123—12232no—
493C2×C4⋊C4—618no—
494C2×C4⋊C4—1224no—
495C2×C4⋊C4—1224no—
496C2×C4⋊C4—1224no—
497C2×C4⋊C4—1224no—
498C2×C4⋊C4—2442no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—618no—
502C2×C22⋊C4—1224no—
503C2×C22⋊C4—1224no—
504C2×C22⋊C4—1224no—
505C2×C22⋊C4—1222no—
506C2×C22⋊C4—1222no—
507C2×C22⋊C4—1222no—
508C2×C22⋊C4—1224no—
509C2×C22⋊C4—1222no—
510C2×C22⋊C4—1222no—
511C2×C22⋊C4—1224no—
512C2×C22⋊C4—2442no—
513C2×C22⋊C4—2442no—
514C2×C22⋊C4C4×D6114yes—
515C2×C22⋊C4D24414yes—
516C2×C22⋊C4D24414yes—
517C2×C22⋊C4C22⋊D6114yes—
518C2×C42—24no—
519C2×C42—24no—
520C2×C42—42no—
521#95—24no—
522#95—1224no—
523#95—1224no—
524#95—1224no—
525#95—1224no—
526#95—1224no—
527#95—1224no—
528#95—1222no—
529#95—1222no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—612no—
535C24—1221no—
536C24—1221no—
537C24—1221no—
538C24—1221no—
539C24—1222no—
540C24—1222no—
541C24—1221no—
542C24—1221no—
543C24—1222no—
544C24—1222no—
545C24C2×C4×D6112yes—
546C24C2×D24412yes—
547C24C2×D24412yes—
548C24C2×D24412yes—
549C24#1175822212yes—
550C24#1175822212yes—
551C24C2×C22⋊D6112yes—
552C24C23×D6111yescharacteristic
553C2×D4—1228no—
554C2×D4—1228no—
555C2×D4—1228no—
556C2×D4—2444no—
557C2×D4—2444no—
558C2×D4—2444no—
559C2×D4—2444no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—28no—
578C22×C4—28no—
579C22×C4—44no—
580C22×C4—48no—
581C22×C4—48no—
582C22×C4—614no—
583C22×C4—612no—
584C22×C4—614no—
585C22×C4—1228no—
586C22×C4—1222no—
587C22×C4—1221no—
588C22×C4—1222no—
589C22×C4—1222no—
590C22×C4—1222no—
591C22×C4—1221no—
592C22×C4—1221no—
593C22×C4—1222no—
594C22×C4—1222no—
595C22×C4—1222no—
596C22×C4—1221no—
597C22×C4—1222no—
598C22×C4—1222no—
599C22×C4—1222no—
600C22×C4—1221no—
601C22×C4—1221no—
602C22×C4—1222no—
603C22×C4—1222no—
604C22×C4—1228no—
605C22×C4—1228no—
606C22×C4—1228no—
607C22×C4—1221no—
608C22×C4—1221no—
609C22×C4—1221no—
610C22×C4—1221no—
611C22×C4—1221no—
612C22×C4—1221no—
613C22×C4—1222no—
614C22×C4—1222no—
615C22×C4—1222no—
616C22×C4—1222no—
617C22×C4—2448no—
618C22×C4—2448no—
619C22×C4—2444no—
620C22×C4—2444no—
621C22×C4—2444no—
622C22×C4—2444no—
623C22×C4—2444no—
624C22×C4—2444no—
625C22×C4C2×C4×D6114yes—
626C22×C4C2×D24414yes—
627C22×C4C2×D24412yes—
628C22×C4C2×D24414yes—
629C22×C4C2×D24412yes—
630C22×C4#1175822414yes—
631C22×C4C2×C22⋊D6114yes—
632C4⋊C4—12216no—
633C4⋊C4—2448no—
634C22⋊C4—28no—
635C22⋊C4—12216no—
636C22⋊C4—2448no—
637C22⋊C4—2444no—
638C22⋊C4—2444no—
639C22⋊C4—2444no—
640C22⋊C4#11758198116yescomplemented
641C42—48no—
642C23—24no—
643C23—24no—
644C23—22no—
645C23—22no—
646C23—24no—
647C23—22no—
648C23—22no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—1222no—
659C23—1222no—
660C23—1222no—
661C23—1224no—
662C23—1224no—
663C23—2441no—
664C23—2441no—
665C23—2441no—
666C23—2441no—
667C23—2441no—
668C23—2442no—
669C23—2441no—
670C23—2441no—
671C23—2441no—
672C23—2442no—
673C23—2442no—
674C23—2442no—
675C23—2442no—
676C23—2442no—
677C23—2442no—
678C23—2442no—
679C23—2442no—
680C23—2442no—
681C23C2×#1175819814yes—
682C23C4×D24414yes—
683C23C4×D24414yes—
684C23#1451975114yes—
685C23#1451975114yes—
686C23#1451976514yes—
687C23#1451977414yes—
688C23C22×C4×D6111yescharacteristic
689C23C22×C22⋊D6111yescharacteristic
690C23C22×D24411yescharacteristic
691C23C22×D24411yescharacteristic
692C23C22×D24411yescharacteristic
693C23#41×D6112yes—
694C23C2×#1175822412yes—
695C23C2×#1175822211yescharacteristic
696C23C2×#1175822211yescharacteristic
697C23#1451982212yes—
698C23#1451982412yes—
699D4—24416no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—416no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—1224no—
724C2×C4—1222no—
725C2×C4—1224no—
726C2×C4—1224no—
727C2×C4—1222no—
728C2×C4—1222no—
729C2×C4—1224no—
730C2×C4—1224no—
731C2×C4—1224no—
732C2×C4—2441no—
733C2×C4—2441no—
734C2×C4—2441no—
735C2×C4—2441no—
736C2×C4—2441no—
737C2×C4—2441no—
738C2×C4—2442no—
739C2×C4—2442no—
740C2×C4—2442no—
741C2×C4—2442no—
742C2×C4—24416no—
743C2×C4—2442no—
744C2×C4—2442no—
745C2×C4—2441no—
746C2×C4—2441no—
747C2×C4—2442no—
748C2×C4—2441no—
749C2×C4—2442no—
750C2×C4—2442no—
751C2×C4—2441no—
752C2×C4—2442no—
753C2×C4—2442no—
754C2×C4—2442no—
755C2×C4—24416no—
756C2×C4C2×#1175819818yes—
757C2×C4#1451976114yescomplemented
758C22—24no—
759C22—24no—
760C22—24no—
761C22—28no—
762C22—28no—
763C22—24no—
764C22—28no—
765C22—28no—
766C22—24no—
767C22—24no—
768C22—4881no—
769C22—4881no—
770C22—4882no—
771C22—4882no—
772C22—4881no—
773C22—4881no—
774C22—2442no—
775C22—2442no—
776C22—2444no—
777C22—2442no—
778C22—2444no—
779C22#1683966418yes—
780C22C22×#1175819811yescharacteristic
781C22C2×C4×D24411yescharacteristic
782C22C2×C4×D24411yescharacteristic
783C22C4×#1175822412yes—
784C22#1684024112yes—
785C22C2×#1451975111yescharacteristic
786C22C2×#1451975111yescharacteristic
787C22C2×#1451976111yescharacteristic
788C22#1684027411yescharacteristic
789C22C2×#1451976511yescharacteristic
790C22#1684029212yes—
791C22C2×#1451977411yescharacteristic
792C22#1684032411yescharacteristic
793C22#1684033811yescharacteristic
794C22#1684035412yes—
795C22#1684040612yes—
796C22#1684040712yes—
797C22#1684040712yes—
798C22#1684041112yes—
799C22#1684041612yes—
800C22#1684041612yes—
801C22#1684043812yes—
802C22#1684044512yes—
803C4—28no—
804C4—24no—
805C4—44no—
806C4—42no—
807C4—4881no—
808C4—4881no—
809C4—2444no—
810C4—2442no—
811C4—2444no—
812C2—28no—
813C2—4882no—
814C2C2×#1683966411yescharacteristic
815C2C4×#1451976111yescharacteristic
816C2#2144849011yescharacteristic
817C2#2144864412yes—
818C2#2144881312yes—
819C2#2144920911yescharacteristic
820C2#2144922011yescharacteristic
821C2#2144936412yes—
822C2#2145013912yes—
823C2#2145029011yescharacteristic
824C2#2145074511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C4×C22⋊C4×C61C2
socle, cosocleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenterC2×C4×C22⋊C4D61
hypocenterC61#13996
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×#16839637C2semidirect
5. C2×#16839623C2semidirect
6. C22×#14519684C2semidirect
7. #21444086C2semidirect
8. #21444065C2semidirect
9. #21444057C2semidirect
10. #21444049C2semidirect
11. C2×C4×C22⋊C4×C61C2semidirect
17. C2×#14519761C4semidirect
75. C2×C4⋊Dic61C2×C4semidirect
88. C2×#11758198C2×C4semidirect
220. C22⋊C4×C61C22⋊C4semidirect
310. C2×C4×C61#123semidirect
405. C2×C4×C22⋊C4D61semidirect
456. C61#13996semidirect
640. C22⋊C4#11758198semidirect
757. C2×C4#14519761semidirect

Maximal subgroups

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

subgroupindex
C22×#145197612
C2×#168396412
C2×#168396392
C2×#168396372
C2×#168396232
C22×#145196842
#214440862
#214440652
#214440572
#214440492
C2×C4×C22⋊C4×C612
#1399661