Finite Group Databasebeta

← #29852883

Subgroups — #29852883

Order 15616.

3754 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840324C212yesmaximal, complemented
2C22×#14519751C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊D61C211yesmaximal, characteristic, complemented
4#21454151C212yesmaximal, complemented
5#21454102C212yesmaximal, complemented
6#21451564C212yesmaximal, complemented
7#21451556C212yesmaximal, complemented
8#21450779C214yesmaximal, complemented
9#21450711C214yesmaximal, complemented
10#21450128C212yesmaximal, complemented
11#21449253C214yesmaximal, complemented
12#21449176C212yesmaximal, complemented
13#21448394C212yesmaximal, complemented
14C2×C61×#380C211yesmaximal, characteristic, complemented
15C23×D244C2211yescharacteristic, complemented
16C23×C22⋊D61C2212yes—
17C23×C22⋊D61C2211yescharacteristic
18C23×C4×D61C2211yescharacteristic, complemented
19#16840324—216no—
20C2×#14519761C2214yes—
21C2×#14519761C2214yescomplemented
22C2×#14519752C2214yescomplemented
23C2×#14519751—28no—
24C2×#14519751C2212yes—
25C2×#14519751C2212yes—
26C2×#14519751C2212yescomplemented
27C2×#14519751C2218yescomplemented
28C2×#14519751C2212yescomplemented
29C2×#14519747C2214yes—
30C2×#14519747C2214yescomplemented
31C2×C4×C22⋊D61—28no—
32C2×C4×C22⋊D61C2212yes—
33C2×C4×C22⋊D61C2212yes—
34C2×C4×C22⋊D61C2212yescomplemented
35C2×C4×C22⋊D61C2212yescomplemented
36C22×C4⋊Dic61C2211yescharacteristic, complemented
37C22×#11758196C2211yescharacteristic, complemented
38C22×C22⋊Dic61C2211yescharacteristic
39C22×#11758198C2211yescharacteristic, complemented
40C22×#11758198C2212yescomplemented
41C22×C4×Dic61C2211yescharacteristic, complemented
42#16839694C2214yescomplemented
43#16839689C2214yescomplemented
44#16839684C2218yescomplemented
45#16839680C2214yescomplemented
46#16839679C2218yescomplemented
47#16839672C2214yescomplemented
48#16839663C2214yescomplemented
49#16839661C2214yescomplemented
50#16839654C2218yescomplemented
51#16839641C2218yescomplemented
52#16839640C2218yescomplemented
53#16839639C2214yescomplemented
54#16839639C2214yescomplemented
55#16839623C2214yescomplemented
56#16839619C2214yescomplemented
57#16839617C2214yescomplemented
58C24×C4×C61C2211yescharacteristic
59C22×C4⋊C4×C61C2212yescomplemented
60C22×C22⋊C4×C61C2212yes—
61C61×#380C2212yescomplemented
62C61×#380C2212yescomplemented
63C61×#380C2212yescomplemented
64C61×#380C2212yescomplemented
65C2×#95×C61C2212yescomplemented
66C24×D61C2312yes—
67C24×D61C2311yescharacteristic
68C22×D244—24no—
69C22×D244—44no—
70C22×D244C2312yes—
71C22×D244C2312yes—
72C22×D244C2318yes—
73C22×C22⋊D61—24no—
74C22×C22⋊D61—24no—
75C22×C22⋊D61—28no—
76C22×C22⋊D61—28no—
77C22×C22⋊D61—28no—
78C22×C22⋊D61D418yescomplemented
79C22×C22⋊D61C2314yes—
80C22×C22⋊D61C2314yes—
81C22×C22⋊D61C2312yes—
82C22×C22⋊D61C2312yes—
83C23×Dic61C2312yes—
84C23×Dic61C2311yescharacteristic
85C23×Dic61C2311yescharacteristic
86C23×Dic61C2311yescharacteristic
87C22×C4×D61—24no—
88C22×C4×D61—44no—
89C22×C4×D61C2312yes—
90C22×C4×D61C2312yes—
91#14519761—216no—
92#14519761—216no—
93#14519752—48no—
94#14519751—28no—
95#14519751—28no—
96#14519751—28no—
97#14519751—28no—
98#14519751—232no—
99#14519747—216no—
100#14519747—216no—
101C4×C22⋊D61—28no—
102C4×C22⋊D61—28no—
103C4×C22⋊D61—28no—
104C4×C22⋊D61—28no—
105C2×C4⋊Dic61—24no—
106C2×C4⋊Dic61C2318yes—
107C2×C4⋊Dic61C2312yes—
108C2×C4⋊Dic61C2312yes—
109C2×#11758196—24no—
110C2×#11758196C2312yes—
111C2×#11758196C2312yes—
112C2×C22⋊Dic61—24no—
113C2×C22⋊Dic61C2312yes—
114C2×C22⋊Dic61C2312yes—
115C2×#11758198—24no—
116C2×#11758198—28no—
117C2×#11758198C2318yes—
118C2×#11758198C2314yes—
119C2×#11758198C2312yes—
120C2×#11758198C2318yes—
121C2×#11758198C2312yes—
122C2×#11758198C2314yes—
123C2×#11758198C2318yes—
124C2×#11758198C2318yes—
125C2×C4×Dic61—24no—
126C2×C4×Dic61C2312yes—
127C2×C4×Dic61C2312yes—
128#14519684C2318yes—
129#14519684C2318yes—
130C25×C61C2311yescharacteristic
131C23×C4×C61—44no—
132C23×C4×C61D418yescomplemented
133C23×C4×C61C2311yescharacteristic
134C23×C4×C61C2311yescharacteristic
135C23×C4×C61C2311yescharacteristic
136C23×C4×C61C2314yes—
137C23×C4×C61C2311yescharacteristic
138C23×C4×C61C2311yescharacteristic
139C23×C4×C61C2311yescharacteristic
140C2×C4⋊C4×C61—44no—
141C2×C4⋊C4×C61C2314yes—
142C2×C4⋊C4×C61C2314yes—
143C2×C22⋊C4×C61—28no—
144C2×C22⋊C4×C61C2314yes—
145C2×C22⋊C4×C61C2314yes—
146#95×C61C2314yes—
147#95×C61C2314yes—
148C24×C61—42no—
149C24×C61—42no—
150C24×C61C2×D414yes—
151C24×C61C2×D414yes—
152C24×C61#4114yes—
153C24×C61C2411yescharacteristic
154C24×C61C2411yescharacteristic
155C24×C61C2411yescharacteristic
156C23×D61—22no—
157C23×D61—22no—
158C23×D61—24no—
159C23×D61—24no—
160C23×D61—24no—
161C23×D61—42no—
162C23×D61—42no—
163C23×D61—44no—
164C23×D61—44no—
165C23×D61C2×D414yescomplemented
166C23×D61C2414yes—
167C23×D61C2412yes—
168C22×C4×C61—24no—
169C22×C4×C61—24no—
170C22×C4×C61—24no—
171C22×C4×C61—28no—
172C22×C4×C61—416no—
173C22×C4×C61—42no—
174C22×C4×C61—42no—
175C22×C4×C61—42no—
176C22×C4×C61—44no—
177C22×C4×C61—44no—
178C22×C4×C61C2×D414yes—
179C22×C4×C61C2×D414yes—
180C22×C4×C61C2×D414yes—
181C22×C4×C61C2×D414yes—
182C22×C4×C61C2×D414yes—
183C22×C4×C61C2×D414yes—
184C22×C4×C61C2418yes—
185C22×C4×C61C2411yescharacteristic
186C22×C4×C61C2411yescharacteristic
187C22×C4×C61C2411yescharacteristic
188C22×C4×C61C2411yescharacteristic
189C2×C22⋊D61—232no—
190C2×C22⋊D61—24no—
191C2×C22⋊D61—24no—
192C2×C22⋊D61—24no—
193C2×C22⋊D61—24no—
194C2×C22⋊D61—28no—
195C2×C22⋊D61—28no—
196C2×C22⋊D61—28no—
197C2×C22⋊D61—28no—
198C2×C22⋊D61—28no—
199C2×C22⋊D61—28no—
200C2×C22⋊D61—432no—
201C2×C22⋊D61C2×D418yes—
202C2×C22⋊D61C2×D418yescomplemented
203C22×Dic61—22no—
204C22×Dic61—22no—
205C22×Dic61—22no—
206C22×Dic61—24no—
207C22×Dic61—24no—
208C22×Dic61—22no—
209C22×Dic61—24no—
210C22×Dic61—42no—
211C22×Dic61—42no—
212C22×Dic61C2×D414yescomplemented
213C22×Dic61C2412yes—
214C22×Dic61C2414yes—
215C22×Dic61C2412yes—
216C22×Dic61C2412yes—
217C2×D244—24no—
218C2×D244—24no—
219C2×D244—28no—
220C2×D244—216no—
221C2×D244—44no—
222C2×D244—416no—
223C2×D244—48no—
224C2×D244—48no—
225C2×C4×D61—24no—
226C2×C4×D61—24no—
227C2×C4×D61—28no—
228C2×C4×D61—44no—
229C2×C4×D61—416no—
230C4⋊C4×C61—28no—
231C4⋊C4×C61—44no—
232C22⋊C4×C61—28no—
233C22⋊C4×C61—28no—
234C22⋊Dic61—24no—
235C22⋊Dic61—24no—
236#11758198—216no—
237#11758198—24no—
238#11758198—24no—
239#11758198—28no—
240#11758198—28no—
241#11758198—216no—
242#11758198—48no—
243#11758198—48no—
244C4⋊Dic61—24no—
245C4⋊Dic61—24no—
246C4⋊Dic61—216no—
247#11758196—24no—
248#11758196—24no—
249C4×Dic61—24no—
250C4×Dic61—24no—
251C23×C61—22no—
252C23×C61—22no—
253C23×C61—22no—
254C23×C61—22no—
255C23×C61—22no—
256C23×C61—22no—
257C23×C61—44no—
258C23×C61—44no—
259C23×C61—48no—
260C23×C61—48no—
261C23×C61#121116yescomplemented
262C23×C61C22×D412yes—
263C23×C61C22×D412yes—
264C23×C61C22×D412yes—
265C23×C61C22×D412yes—
266C23×C61C22×D412yes—
267C23×C61C22×D412yes—
268C23×C61C2×#4112yes—
269C23×C61C2×#4112yes—
270C23×C61C2×#4112yes—
271C23×C61C2511yescharacteristic
272C22×D61—28no—
273C22×D61—22no—
274C22×D61—22no—
275C22×D61—24no—
276C22×D61—24no—
277C22×D61—24no—
278C22×D61—24no—
279C22×D61—24no—
280C22×D61—28no—
281C22×D61—28no—
282C22×D61—48no—
283C22×D61—44no—
284C22×D61—44no—
285C22×D61—48no—
286C22×D61—48no—
287C22×D61—48no—
288C22×D61—48no—
289C22×D61—88no—
290C22×D61—88no—
291C22×D61C22×D414yes—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—28no—
296C2×C4×C61—28no—
297C2×C4×C61—28no—
298C2×C4×C61—28no—
299C2×C4×C61—28no—
300C2×C4×C61—28no—
301C2×C4×C61—44no—
302C2×C4×C61—44no—
303C2×C4×C61—44no—
304C2×C4×C61—88no—
305C2×C4×C61C22×D412yes—
306C2×C4×C61C22×D412yes—
307C2×C4×C61C22×D412yes—
308C2×C4×C61C22×D412yes—
309C2×C4×C61H(5,𝔽2)14yes—
310C22⋊D61—216no—
311C22⋊D61—216no—
312C22⋊D61—416no—
313C22⋊D61—416no—
314C2×Dic61—28no—
315C2×Dic61—22no—
316C2×Dic61—22no—
317C2×Dic61—22no—
318C2×Dic61—22no—
319C2×Dic61—24no—
320C2×Dic61—24no—
321C2×Dic61—24no—
322C2×Dic61—24no—
323C2×Dic61—24no—
324C2×Dic61—44no—
325C2×Dic61—44no—
326C2×Dic61—48no—
327C2×Dic61C22×D414yes—
328D244—48no—
329D244—48no—
330D244—816no—
331C4×D61—48no—
332C4×D61—48no—
333#35000—611nomaximal, Sylow
334C22×C61—22no—
335C22×C61—22no—
336C22×C61—22no—
337C22×C61—22no—
338C22×C61—22no—
339C22×C61—22no—
340C22×C61—24no—
341C22×C61—24no—
342C22×C61—24no—
343C22×C61—24no—
344C22×C61—24no—
345C22×C61—24no—
346C22×C61—416no—
347C22×C61C2×#12114yes—
348C22×C61C2×#12114yes—
349C22×C61C2×#12114yes—
350C22×C61C23×D411yescharacteristic
351C22×C61C23×D411yescharacteristic
352C22×C61C22×#4111yescharacteristic
353C22×C61C2×H(5,𝔽2)12yes—
354C22×C61#58512yes—
355C2×D61—24no—
356C2×D61—28no—
357C2×D61—416no—
358C2×D61—42no—
359C2×D61—42no—
360C2×D61—44no—
361C2×D61—44no—
362C2×D61—44no—
363C2×D61—44no—
364C2×D61—48no—
365C2×D61—48no—
366C2×D61—816no—
367C4×C61—22no—
368C4×C61—22no—
369C4×C61—22no—
370C4×C61—48no—
371C4×C61#53414yescomplemented
372Dic61—24no—
373Dic61—44no—
374Dic61—42no—
375Dic61—42no—
376C2×#534—612no—
377C22×#121—611no—
378C22×C4×D4—611no—
379#2854—612no—
380#2847—612no—
381#2618—612no—
382#2617—612no—
383#2543—614no—
384#2534—614no—
385#2486—612no—
386#2416—614no—
387#2408—612no—
388#2308—612no—
389C2×#380D6111yescharacteristic, complemented
390C2×C61—24no—
391C2×C61—24no—
392C2×C61—24no—
393C2×C61C22×#12111yescharacteristic
394C2×C61C2×#53411yescharacteristic
395C2×C61#344911yescharacteristic
396C2×C61#349612yes—
397C2×C61#350512yes—
398D61—44no—
399D61—84no—
400C23×D4—611no—
401C23×D4—612no—
402C23×D4—611no—
403C24×C4—611no—
404C24×C4C2×D6111yescharacteristic
405#534—12216no—
406C2×#123—614no—
407C2×#123—614no—
408C2×#121—612no—
409C2×#121—612no—
410C2×#121—612no—
411C2×#121—612no—
412C2×#121—618no—
413C2×#121—614no—
414C2×#121—1228no—
415C2×#120—614no—
416C2×#120—614no—
417C2×C4×D4—612no—
418C2×C4×D4—612no—
419C2×C4×D4—612no—
420C2×C4×D4—612no—
421C2×C4×D4—1228no—
422C22×C4⋊C4—611no—
423C22×C4⋊C4—611no—
424C22×C4⋊C4C2×D6112yescomplemented
425C22×C22⋊C4—611no—
426C22×C22⋊C4—611no—
427C22×C22⋊C4—612no—
428C22×C22⋊C4C2×D6112yes—
429C22×C42—611no—
430#398—614no—
431#397—614no—
432#396—618no—
433#394—618no—
434#394—614no—
435#392—614no—
436#390—614no—
437#389—614no—
438#388—618no—
439#386—618no—
440#386—614no—
441#386—614no—
442#386—618no—
443#381—614no—
444#380—614no—
445#380C2×D6112yescomplemented
446#380C2×D6112yescomplemented
447#380C2×D6112yescomplemented
448#380C2×D6112yescomplemented
449#379—614no—
450C2×#95C2×D6112yescomplemented
451C61#3500011yescharacteristic, complemented, Sylow
452C25—611no—
453C25—612no—
454C25C22×D6111yescharacteristic
455C22×D4—618no—
456C22×D4—612no—
457C22×D4—612no—
458C22×D4—614no—
459C22×D4—614no—
460C22×D4—612no—
461C22×D4—618no—
462C22×D4—612no—
463C22×D4—1224no—
464C22×D4—1224no—
465C22×D4—1228no—
466C22×D4—1228no—
467C22×D4—1228no—
468C22×D4—1224no—
469C22×D4—2444no—
470C23×C4—44no—
471C23×C4—611no—
472C23×C4—612no—
473C23×C4—611no—
474C23×C4—611no—
475C23×C4—612no—
476C23×C4—612no—
477C23×C4—1224no—
478C23×C4—2444no—
479C23×C4D24418yescomplemented
480C23×C4C22×D6111yescharacteristic
481C23×C4C22×D6111yescharacteristic
482C23×C4C22×D6111yescharacteristic
483C23×C4C22×D6114yes—
484C23×C4C22×D6111yescharacteristic
485C23×C4C22×D6111yescharacteristic
486C23×C4C22×D6111yescharacteristic
487#123—12216no—
488#123—12216no—
489#121—12232no—
490#121—1228no—
491#121—1228no—
492#121—1228no—
493#121—1228no—
494#121—2448no—
495#120—12216no—
496#120—12216no—
497C4×D4—1228no—
498C4×D4—1228no—
499C4×D4—1228no—
500C4×D4—1228no—
501C2×C4⋊C4—44no—
502C2×C4⋊C4—612no—
503C2×C4⋊C4—612no—
504C2×C4⋊C4—612no—
505C2×C4⋊C4—612no—
506C2×C4⋊C4—618no—
507C2×C4⋊C4—1224no—
508C2×C4⋊C4—1224no—
509C2×C4⋊C4C22×D6114yes—
510C2×C4⋊C4C22×D6114yes—
511C2×C22⋊C4—28no—
512C2×C22⋊C4—612no—
513C2×C22⋊C4—612no—
514C2×C22⋊C4—612no—
515C2×C22⋊C4—612no—
516C2×C22⋊C4—614no—
517C2×C22⋊C4—614no—
518C2×C22⋊C4—618no—
519C2×C22⋊C4—618no—
520C2×C22⋊C4—618no—
521C2×C22⋊C4—618no—
522C2×C22⋊C4—1224no—
523C2×C22⋊C4—1224no—
524C2×C22⋊C4—1228no—
525C2×C22⋊C4C22×D6114yes—
526C2×C22⋊C4C22×D6114yes—
527C2×C42—612no—
528C2×C42—612no—
529C2×C42—1224no—
530#95—618no—
531#95—618no—
532#95C22×D6114yes—
533#95C22×D6114yes—
534C24—42no—
535C24—42no—
536C24—612no—
537C24—614no—
538C24—614no—
539C24—1222no—
540C24—1222no—
541C24—1224no—
542C24—1224no—
543C24—1224no—
544C24—2444no—
545C24—2444no—
546C24—2442no—
547C24—2442no—
548C24C2×D24414yes—
549C24D4×D6114yes—
550C24#1175822614yes—
551C24C23×D6111yescharacteristic
552C24C23×D6111yescharacteristic
553C24C23×D6111yescharacteristic
554C2×D4—618no—
555C2×D4—618no—
556C2×D4—12216no—
557C2×D4—1224no—
558C2×D4—1224no—
559C2×D4—1224no—
560C2×D4—1224no—
561C2×D4—12232no—
562C2×D4—1228no—
563C2×D4—1228no—
564C2×D4—1228no—
565C2×D4—1228no—
566C2×D4—1228no—
567C2×D4—1228no—
568C2×D4—1224no—
569C2×D4—1224no—
570C2×D4—1228no—
571C2×D4—2448no—
572C2×D4—2448no—
573C2×D4—2444no—
574C2×D4—24416no—
575C2×D4—24432no—
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—28no—
580C22×C4—416no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—614no—
587C22×C4—612no—
588C22×C4—612no—
589C22×C4—612no—
590C22×C4—614no—
591C22×C4—1222no—
592C22×C4—1222no—
593C22×C4—1224no—
594C22×C4—1222no—
595C22×C4—1222no—
596C22×C4—1224no—
597C22×C4—1224no—
598C22×C4—1224no—
599C22×C4—1224no—
600C22×C4—1228no—
601C22×C4—2444no—
602C22×C4—24416no—
603C22×C4—2442no—
604C22×C4—2442no—
605C22×C4C2×D24414yes—
606C22×C4C2×D24414yes—
607C22×C4C2×D24414yes—
608C22×C4C2×D24414yes—
609C22×C4C2×D24414yes—
610C22×C4C2×D24414yes—
611C22×C4C23×D6118yes—
612C22×C4C23×D6111yescharacteristic
613C22×C4C23×D6111yescharacteristic
614C22×C4C23×D6111yescharacteristic
615C22×C4C23×D6111yescharacteristic
616C4⋊C4—28no—
617C4⋊C4—44no—
618C4⋊C4—12216no—
619C4⋊C4—1224no—
620C4⋊C4—1224no—
621C4⋊C4—1224no—
622C4⋊C4—1224no—
623C22⋊C4—28no—
624C22⋊C4—28no—
625C22⋊C4—12216no—
626C22⋊C4—12216no—
627C22⋊C4—1224no—
628C22⋊C4—1224no—
629C22⋊C4—1224no—
630C22⋊C4—1224no—
631C22⋊C4—1228no—
632C22⋊C4—1228no—
633C22⋊C4—2448no—
634C22⋊C4—2448no—
635C42—1224no—
636C42—1224no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—44no—
644C23—44no—
645C23—48no—
646C23—48no—
647C23—614no—
648C23—1228no—
649C23—1222no—
650C23—1222no—
651C23—1224no—
652C23—1224no—
653C23—1224no—
654C23—1224no—
655C23—1224no—
656C23—1228no—
657C23—1228no—
658C23—4888no—
659C23—4888no—
660C23—2448no—
661C23—2448no—
662C23—2448no—
663C23—2444no—
664C23—2448no—
665C23—2444no—
666C23—2448no—
667C23#14519752116yescomplemented
668C23C2×D4×D6112yes—
669C23C2×D4×D6112yes—
670C23C2×D4×D6112yes—
671C23C22×D24412yes—
672C23C22×D24412yes—
673C23C22×D24412yes—
674C23C2×#1175822612yes—
675C23C2×#1175822612yes—
676C23C2×#1175822612yes—
677C23C24×D6111yescharacteristic
678D4—12216no—
679D4—12216no—
680D4—48816no—
681D4—2448no—
682D4—24416no—
683D4—24416no—
684D4—2448no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—28no—
689C2×C4—28no—
690C2×C4—28no—
691C2×C4—28no—
692C2×C4—28no—
693C2×C4—28no—
694C2×C4—44no—
695C2×C4—44no—
696C2×C4—44no—
697C2×C4—88no—
698C2×C4—614no—
699C2×C4—1228no—
700C2×C4—1222no—
701C2×C4—1222no—
702C2×C4—1224no—
703C2×C4—1222no—
704C2×C4—1222no—
705C2×C4—1224no—
706C2×C4—1224no—
707C2×C4—1224no—
708C2×C4—1224no—
709C2×C4—2448no—
710C2×C4—2444no—
711C2×C4—2444no—
712C2×C4—2448no—
713C2×C4—2448no—
714C2×C4C22×D24412yes—
715C2×C4C22×D24412yes—
716C2×C4C22×D24412yes—
717C2×C4C22×D24412yes—
718C2×C4#1451982214yes—
719C22—24no—
720C22—24no—
721C22—24no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—24no—
726C22—24no—
727C22—24no—
728C22—22no—
729C22—22no—
730C22—22no—
731C22—416no—
732C22—1224no—
733C22—1228no—
734C22—48816no—
735C22—24416no—
736C22—2444no—
737C22—2448no—
738C22—2444no—
739C22—2448no—
740C22—2444no—
741C22—2442no—
742C22—2444no—
743C22—2442no—
744C22C2×#1451975214yes—
745C22C2×#1451975214yes—
746C22C2×#1451975214yes—
747C22C22×D4×D6111yescharacteristic
748C22C23×D24411yescharacteristic
749C22C22×#1175822611yescharacteristic
750C22C2×#1451982212yes—
751C22#1684059812yes—
752C4—22no—
753C4—22no—
754C4—22no—
755C4—48no—
756C4—1224no—
757C4—2444no—
758C4—2442no—
759C4—2442no—
760C4#1684032414yescomplemented
761C2—24no—
762C2—24no—
763C2—24no—
764C2—4884no—
765C2—2444no—
766C2C22×#1451975211yescharacteristic
767C2C2×#1684032411yescharacteristic
768C2#2145915211yescharacteristic
769C2#2145957612yes—
770C2#2145966012yes—
subgroupG/H
center, FrattiniC23C24×D61
commutator, socle, cosocleC23×C61C25
FittingC2×C61×#380C2
hypercenterC2×#380D61
hypocenterC61#35000
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
1. C2×#16840324C2semidirect
2. C22×#14519751C2semidirect
3. C22×C4×C22⋊D61C2semidirect
4. #21454151C2semidirect
5. #21454102C2semidirect
6. #21451564C2semidirect
7. #21451556C2semidirect
8. #21450779C2semidirect
9. #21450711C2semidirect
10. #21450128C2semidirect
11. #21449253C2semidirect
12. #21449176C2semidirect
13. #21448394C2semidirect
14. C2×C61×#380C2semidirect
15. C23×D244C22semidirect
18. C23×C4×D61C22semidirect
21. C2×#14519761C22semidirect
22. C2×#14519752C22semidirect
26. C2×#14519751C22semidirect
27. C2×#14519751C22semidirect
28. C2×#14519751C22semidirect
30. C2×#14519747C22semidirect
34. C2×C4×C22⋊D61C22semidirect
35. C2×C4×C22⋊D61C22semidirect
36. C22×C4⋊Dic61C22semidirect
37. C22×#11758196C22semidirect
39. C22×#11758198C22semidirect
40. C22×#11758198C22semidirect
41. C22×C4×Dic61C22semidirect
42. #16839694C22semidirect
43. #16839689C22semidirect
44. #16839684C22semidirect
45. #16839680C22semidirect
46. #16839679C22semidirect
47. #16839672C22semidirect
48. #16839663C22semidirect
49. #16839661C22semidirect
50. #16839654C22semidirect
51. #16839641C22semidirect
52. #16839640C22semidirect
53. #16839639C22semidirect
54. #16839639C22semidirect
55. #16839623C22semidirect
56. #16839619C22semidirect
57. #16839617C22semidirect
59. C22×C4⋊C4×C61C22semidirect
61. C61×#380C22semidirect
62. C61×#380C22semidirect
63. C61×#380C22semidirect
64. C61×#380C22semidirect
65. C2×#95×C61C22semidirect
78. C22×C22⋊D61D4semidirect
132. C23×C4×C61D4semidirect
165. C23×D61C2×D4semidirect
202. C2×C22⋊D61C2×D4semidirect
212. C22×Dic61C2×D4semidirect
261. C23×C61#121semidirect
371. C4×C61#534semidirect
389. C2×#380D61semidirect
424. C22×C4⋊C4C2×D61semidirect
445. #380C2×D61semidirect
446. #380C2×D61semidirect
447. #380C2×D61semidirect
448. #380C2×D61semidirect
450. C2×#95C2×D61semidirect
451. C61#35000semidirect
479. C23×C4D244semidirect
667. C23#14519752semidirect
760. C4#16840324semidirect

Maximal subgroups

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

subgroupindex
C2×#168403242
C22×#145197512
C22×C4×C22⋊D612
#214541512
#214541022
#214515642
#214515562
#214507792
#214507112
#214501282
#214492532
#214491762
#214483942
C2×C61×#3802
#3500061