Finite Group Databasebeta

← #29607225

Subgroups — #29607225

Order 15616.

2150 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D61C211yesmaximal, characteristic
2C2×#16839629C211yesmaximal, characteristic, complemented
3C2×#16839626C211yesmaximal, characteristic, complemented
4#21444085C212yesmaximal, complemented
5#21444063C212yesmaximal, complemented
6#21444062C212yesmaximal, complemented
7#21444058C212yesmaximal
8#21444042C211yesmaximal, characteristic, complemented
9#21444040C211yesmaximal, characteristic, complemented
10#21444040C211yesmaximal, characteristic, complemented
11C61×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×C22⋊D61C2211yescharacteristic
13C23×C4×D61C2211yescharacteristic
14C2×C4×C22⋊D61—24no—
15C2×C4×C22⋊D61—24no—
16C2×C4×C22⋊D61C418yescomplemented
17C22×#11758196C2211yescharacteristic
18C22×#11758196C2212yes—
19C22×C22⋊Dic61C2211yescharacteristic
20C22×C22⋊Dic61C2212yes—
21C22×#11758198C2211yescharacteristic
22C22×#11758198C2212yes—
23C22×#11758198C2212yes—
24C22×C4×Dic61C2211yescharacteristic
25#16839629—24no—
26#16839626—24no—
27C2×#14519684C2211yescharacteristic
28C2×#14519684C2212yes—
29C2×#14519684C2211yescharacteristic
30C2×#14519684C2212yes—
31C2×#14519684C2212yes—
32C2×#14519684C2212yes—
33C2×#14519684C2212yes—
34C2×#14519684C2212yes—
35C24×C4×C61C2211yescharacteristic
36C22×C22⋊C4×C61C2212yes—
37C2×#95×C61C2211yescharacteristic
38C2×#95×C61C2211yescharacteristic
39C2×#95×C61C2212yes—
40C24×D61C2311yescharacteristic
41C22×C22⋊D61—24no—
42C22×C22⋊D61—24no—
43C22×C22⋊D61—22no—
44C22×C22⋊D61—22no—
45C22×C22⋊D61C2×C414yes—
46C23×Dic61C2312yes—
47C23×Dic61C2312yes—
48C23×Dic61C2311yescharacteristic
49C23×Dic61C2311yescharacteristic
50C23×Dic61C2311yescharacteristic
51C22×C4×D61—22no—
52C22×C4×D61—22no—
53C22×C4×D61—42no—
54C22×C4×D61—42no—
55C22×C4×D61C2×C414yes—
56C4×C22⋊D61—232no—
57C2×#11758196—22no—
58C2×#11758196—22no—
59C2×#11758196—24no—
60C2×#11758196—42no—
61C2×#11758196—42no—
62C2×#11758196C2×C414yes—
63C2×C22⋊Dic61—22no—
64C2×C22⋊Dic61—22no—
65C2×C22⋊Dic61—24no—
66C2×C22⋊Dic61—42no—
67C2×C22⋊Dic61—42no—
68C2×C22⋊Dic61C2×C414yes—
69C2×#11758198—22no—
70C2×#11758198—22no—
71C2×#11758198—24no—
72C2×#11758198—24no—
73C2×#11758198—42no—
74C2×#11758198—42no—
75C2×#11758198—42no—
76C2×#11758198—42no—
77C2×#11758198C2×C414yes—
78C2×C4×Dic61C2×C414yes—
79C2×C4×Dic61D414yes—
80C2×C4×Dic61D414yes—
81#14519684—22no—
82#14519684—22no—
83#14519684—24no—
84#14519684—24no—
85#14519684—24no—
86#14519684—42no—
87#14519684—42no—
88#14519684—42no—
89C25×C61C2311yescharacteristic
90C23×C4×C61—22no—
91C23×C4×C61—22no—
92C23×C4×C61—42no—
93C23×C4×C61—42no—
94C23×C4×C61C2×C414yes—
95C23×C4×C61C2312yes—
96C23×C4×C61C2312yes—
97C23×C4×C61C2311yescharacteristic
98C23×C4×C61C2311yescharacteristic
99C2×C22⋊C4×C61—24no—
100C2×C22⋊C4×C61—42no—
101C2×C22⋊C4×C61—42no—
102#95×C61—22no—
103#95×C61—22no—
104#95×C61—42no—
105C24×C61—21no—
106C24×C61—21no—
107C24×C61—22no—
108C24×C61—21no—
109C24×C61—22no—
110C24×C61—22no—
111C24×C61—21no—
112C24×C61—21no—
113C24×C61—21no—
114C24×C61C22×C412yes—
115C24×C61#4114yes—
116C24×C61C2411yescharacteristic
117C23×D61—21no—
118C23×D61—21no—
119C23×D61—22no—
120C23×D61—22no—
121C23×D61—22no—
122C23×D61—21no—
123C23×D61—21no—
124C23×D61—21no—
125C23×D61—21no—
126C23×D61C22×C412yes—
127C23×D61#4114yes—
128C22×C4×C61—22no—
129C22×C4×C61—22no—
130C22×C4×C61—21no—
131C22×C4×C61—21no—
132C22×C4×C61—22no—
133C22×C4×C61—22no—
134C22×C4×C61—28no—
135C22×C4×C61—22no—
136C22×C4×C61—22no—
137C22×C4×C61—22no—
138C22×C4×C61—22no—
139C22×C4×C61—22no—
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—44no—
150C22×C4×C61—44no—
151C22×C4×C61—48no—
152C22×C4×C61—48no—
153C22×C4×C61C22×C412yes—
154C22×C4×C61C22×C412yes—
155C22×C4×C61C2×D412yes—
156C22×C4×C61C2×D412yes—
157C2×C22⋊D61—216no—
158C2×C22⋊D61—216no—
159C2×C22⋊D61—28no—
160C2×C22⋊D61—28no—
161C2×C22⋊D61—28no—
162C22×Dic61—22no—
163C22×Dic61—22no—
164C22×Dic61—21no—
165C22×Dic61—21no—
166C22×Dic61—21no—
167C22×Dic61—21no—
168C22×Dic61—21no—
169C22×Dic61—21no—
170C22×Dic61—22no—
171C22×Dic61—22no—
172C22×Dic61—22no—
173C22×Dic61—22no—
174C22×Dic61—22no—
175C22×Dic61—22no—
176C22×Dic61—22no—
177C22×Dic61—22no—
178C22×Dic61—22no—
179C22×Dic61—22no—
180C22×Dic61—22no—
181C22×Dic61—22no—
182C22×Dic61—22no—
183C22×Dic61—22no—
184C22×Dic61—22no—
185C22×Dic61—22no—
186C22×Dic61C22×C412yes—
187C22×Dic61C22×C412yes—
188C22×Dic61C22×C412yes—
189C22×Dic61C2×D412yes—
190C22×Dic61C2×D412yes—
191C22×Dic61C2×D412yes—
192C22×Dic61C2×D412yes—
193C2×C4×D61—28no—
194C2×C4×D61—44no—
195C2×C4×D61—44no—
196C2×C4×D61—48no—
197C2×C4×D61—48no—
198C22⋊C4×C61—48no—
199C22⋊Dic61—28no—
200C22⋊Dic61—48no—
201#11758198—28no—
202#11758198—48no—
203#11758198—48no—
204#11758196—28no—
205#11758196—48no—
206C4×Dic61C22⋊C4116yescomplemented
207C23×C61—22no—
208C23×C61—22no—
209C23×C61—22no—
210C23×C61—22no—
211C23×C61—22no—
212C23×C61—22no—
213C23×C61—24no—
214C23×C61—24no—
215C23×C61—24no—
216C23×C61—24no—
217C23×C61—24no—
218C23×C61—24no—
219C23×C61—42no—
220C23×C61—42no—
221C23×C61—41no—
222C23×C61—41no—
223C23×C61—41no—
224C23×C61—41no—
225C23×C61—42no—
226C23×C61—42no—
227C23×C61—42no—
228C23×C61—42no—
229C23×C61#11714yes—
230C23×C61C23×C411yescharacteristic
231C23×C61C22×D411yescharacteristic
232C23×C61C22×D411yescharacteristic
233C23×C61C2×#4112yes—
234C23×C61C2×#4112yes—
235C23×C61H(5,𝔽2)12yes—
236C23×C61H(5,𝔽2)12yes—
237C23×C61H(5,𝔽2)11yescharacteristic
238C23×C61H(5,𝔽2)11yescharacteristic
239C23×C612−1+411yescharacteristic
240C23×C612−1+411yescharacteristic
241C22×D61—22no—
242C22×D61—22no—
243C22×D61—22no—
244C22×D61—22no—
245C22×D61—22no—
246C22×D61—22no—
247C22×D61—24no—
248C22×D61—24no—
249C22×D61—24no—
250C22×D61—24no—
251C22×D61—24no—
252C22×D61—24no—
253C22×D61—42no—
254C22×D61—42no—
255C22×D61—41no—
256C22×D61—41no—
257C22×D61—41no—
258C22×D61—41no—
259C22×D61—42no—
260C22×D61—42no—
261C22×D61—42no—
262C22×D61—42no—
263C22×D61#11714yes—
264C2×C4×C61—22no—
265C2×C4×C61—22no—
266C2×C4×C61—24no—
267C2×C4×C61—24no—
268C2×C4×C61—22no—
269C2×C4×C61—22no—
270C2×C4×C61—22no—
271C2×C4×C61—416no—
272C2×C4×C61—42no—
273C2×C4×C61—42no—
274C2×C4×C61—42no—
275C2×C4×C61—42no—
276C2×C4×C61—42no—
277C2×C4×C61—42no—
278C2×C4×C61—42no—
279C2×C4×C61—42no—
280C2×C4×C61—42no—
281C2×C4×C61—42no—
282C2×C4×C61—42no—
283C2×C4×C61—42no—
284C2×C4×C61—42no—
285C2×C4×C61—42no—
286C2×C4×C61—42no—
287C2×C4×C61—42no—
288C2×C4×C61C2×C22⋊C414yes—
289C22⋊D61—232no—
290C2×Dic61—22no—
291C2×Dic61—22no—
292C2×Dic61—22no—
293C2×Dic61—22no—
294C2×Dic61—24no—
295C2×Dic61—24no—
296C2×Dic61—22no—
297C2×Dic61—22no—
298C2×Dic61—22no—
299C2×Dic61—22no—
300C2×Dic61—22no—
301C2×Dic61—22no—
302C2×Dic61—22no—
303C2×Dic61—42no—
304C2×Dic61—42no—
305C2×Dic61—42no—
306C2×Dic61—42no—
307C2×Dic61—42no—
308C2×Dic61—42no—
309C2×Dic61—42no—
310C2×Dic61—42no—
311C2×Dic61—42no—
312C2×Dic61—42no—
313C2×Dic61—42no—
314C2×Dic61—42no—
315C2×Dic61—42no—
316C2×Dic61—42no—
317C2×Dic61—42no—
318C2×Dic61—42no—
319C2×Dic61C2×C22⋊C414yes—
320C2×Dic61C2×C22⋊C414yes—
321C4×D61—416no—
322#14345—611nomaximal, Sylow
323C22×C61—24no—
324C22×C61—24no—
325C22×C61—24no—
326C22×C61—42no—
327C22×C61—42no—
328C22×C61—42no—
329C22×C61—42no—
330C22×C61—44no—
331C22×C61—44no—
332C22×C61—44no—
333C22×C61—44no—
334C22×C61C22×C22⋊C411yescharacteristic
335C22×C61C2×#11711yescharacteristic
336C22×C61C2×#11711yescharacteristic
337C22×C61#51811yescharacteristic
338C22×C61#51811yescharacteristic
339C22×C61#52011yescharacteristic
340C22×C61#52011yescharacteristic
341C22×C61#52512yes—
342C22×C61#52512yes—
343C22×C61#53512yes—
344C22×C61#53512yes—
345C22×C61#53511yescharacteristic
346C22×C61#53611yescharacteristic
347C22×C61#53711yescharacteristic
348C22×C61#53711yescharacteristic
349C22×C61#53812yes—
350C22×C61#53812yes—
351C22×C61#53812yes—
352C22×C61#53812yes—
353C22×C61#53912yes—
354C22×C61#53912yes—
355C22×C61#53912yes—
356C22×C61#53912yes—
357C2×D61—24no—
358C2×D61—24no—
359C2×D61—24no—
360C2×D61—42no—
361C2×D61—42no—
362C2×D61—42no—
363C2×D61—42no—
364C2×D61—44no—
365C2×D61—44no—
366C2×D61—44no—
367C2×D61—44no—
368C4×C61—24no—
369C4×C61—42no—
370C4×C61—82no—
371C4×C61—82no—
372Dic61—24no—
373Dic61—24no—
374Dic61—42no—
375Dic61—82no—
376Dic61—82no—
377C22×C4×D4—611no—
378C2×#383—611no—
379C2×#382—611no—
380#1445—612no—
381#1439—612no—
382#1439—612no—
383#1438—612no—
384C22⋊#95—611no—
385C22⋊#95—611no—
386C22⋊#95—611no—
387C22⋊#95D6111yescharacteristic, complemented
388C2×C61—44no—
389C2×C61#228011yescharacteristic
390C2×C61#230911yescharacteristic
391C2×C61#231111yescharacteristic
392C2×C61#231811yescharacteristic
393C2×C61#231811yescharacteristic
394C2×C61#231811yescharacteristic
395C2×C61#231811yescharacteristic
396C2×C61#263112yes—
397C2×C61#263312yes—
398C2×C61#263612yes—
399C2×C61#263612yes—
400D61—44no—
401C23×D4—611no—
402C24×C4—611no—
403C24×C4C2×D6111yescharacteristic
404C2×C4×D4—618no—
405C2×C4×D4—1224no—
406C2×C4×D4—1224no—
407C22×C4⋊C4—611no—
408C22×C4⋊C4—612no—
409C22×C22⋊C4—611no—
410C22×C22⋊C4—611no—
411C22×C22⋊C4—612no—
412C22×C22⋊C4—612no—
413C22×C22⋊C4—612no—
414C22×C22⋊C4C2×D6112yes—
415C22×C42—611no—
416#383—1224no—
417#382—1224no—
418C2×#95—611no—
419C2×#95—611no—
420C2×#95—612no—
421C2×#95—612no—
422C2×#95—612no—
423C2×#95—612no—
424C2×#95—612no—
425C2×#95—612no—
426C2×#95C2×D6111yescharacteristic
427C2×#95C2×D6111yescharacteristic
428C2×#95C2×D6112yes—
429C61#1434511yescharacteristic, complemented, Sylow
430C25—611no—
431C25C22×D6111yescharacteristic
432C22×D4—614no—
433C22×D4—1222no—
434C22×D4—1222no—
435C22×D4—1224no—
436C22×D4—1224no—
437C23×C4—22no—
438C23×C4—22no—
439C23×C4—42no—
440C23×C4—42no—
441C23×C4—611no—
442C23×C4—611no—
443C23×C4—611no—
444C23×C4—614no—
445C23×C4—612no—
446C23×C4—612no—
447C23×C4—1222no—
448C23×C4—1222no—
449C23×C4—2442no—
450C23×C4—2442no—
451C23×C4C4×D6114yes—
452C23×C4C22×D6112yes—
453C23×C4C22×D6112yes—
454C23×C4C22×D6111yescharacteristic
455C23×C4C22×D6111yescharacteristic
456C4×D4—12232no—
457C2×C4⋊C4—614no—
458C2×C4⋊C4—1222no—
459C2×C4⋊C4—1222no—
460C2×C4⋊C4—1224no—
461C2×C4⋊C4—2442no—
462C2×C4⋊C4—2442no—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—42no—
465C2×C22⋊C4—42no—
466C2×C22⋊C4—614no—
467C2×C22⋊C4—614no—
468C2×C22⋊C4—1222no—
469C2×C22⋊C4—1222no—
470C2×C22⋊C4—1222no—
471C2×C22⋊C4—1222no—
472C2×C22⋊C4—1224no—
473C2×C22⋊C4—1224no—
474C2×C22⋊C4—1224no—
475C2×C22⋊C4—2442no—
476C2×C22⋊C4—2442no—
477C2×C22⋊C4—2442no—
478C2×C22⋊C4—2442no—
479C2×C22⋊C4—2442no—
480C2×C22⋊C4—2442no—
481C2×C42—614no—
482C2×C42—614no—
483C2×C42—614no—
484#95—22no—
485#95—22no—
486#95—42no—
487#95—1224no—
488#95—1224no—
489#95—1224no—
490#95—1222no—
491#95—1222no—
492#95—2442no—
493#95—2442no—
494#95—2442no—
495C24—21no—
496C24—21no—
497C24—22no—
498C24—21no—
499C24—22no—
500C24—22no—
501C24—21no—
502C24—21no—
503C24—21no—
504C24—612no—
505C24—614no—
506C24—1221no—
507C24—1221no—
508C24—1222no—
509C24—1221no—
510C24—1222no—
511C24—1222no—
512C24—1221no—
513C24—1221no—
514C24—1221no—
515C24C2×C4×D6112yes—
516C24#1175822214yes—
517C24C23×D6111yescharacteristic
518C2×D4—1228no—
519C2×D4—1228no—
520C2×D4—12216no—
521C2×D4—12216no—
522C2×D4—1228no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—28no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—44no—
545C22×C4—44no—
546C22×C4—48no—
547C22×C4—48no—
548C22×C4—612no—
549C22×C4—612no—
550C22×C4—612no—
551C22×C4—612no—
552C22×C4—612no—
553C22×C4—612no—
554C22×C4—612no—
555C22×C4—1222no—
556C22×C4—1222no—
557C22×C4—1221no—
558C22×C4—1221no—
559C22×C4—1221no—
560C22×C4—1221no—
561C22×C4—1221no—
562C22×C4—1221no—
563C22×C4—1222no—
564C22×C4—1222no—
565C22×C4—1228no—
566C22×C4—1222no—
567C22×C4—1222no—
568C22×C4—1222no—
569C22×C4—1222no—
570C22×C4—1222no—
571C22×C4—1222no—
572C22×C4—1222no—
573C22×C4—1222no—
574C22×C4—1222no—
575C22×C4—1222no—
576C22×C4—1222no—
577C22×C4—1222no—
578C22×C4—1222no—
579C22×C4—1222no—
580C22×C4—2444no—
581C22×C4—2444no—
582C22×C4—2448no—
583C22×C4—2448no—
584C22×C4C2×C4×D6112yes—
585C22×C4C2×C4×D6112yes—
586C22×C4D4×D6112yes—
587C22×C4D4×D6112yes—
588C4⋊C4—1228no—
589C4⋊C4—2448no—
590C22⋊C4—48no—
591C22⋊C4—1228no—
592C22⋊C4—1228no—
593C22⋊C4—2448no—
594C22⋊C4—2448no—
595C22⋊C4—2448no—
596C42—6116no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—24no—
604C23—24no—
605C23—24no—
606C23—24no—
607C23—24no—
608C23—24no—
609C23—42no—
610C23—42no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—614no—
620C23—1222no—
621C23—1222no—
622C23—1222no—
623C23—1222no—
624C23—1222no—
625C23—1222no—
626C23—1224no—
627C23—1224no—
628C23—1224no—
629C23—1224no—
630C23—1224no—
631C23—1224no—
632C23—2442no—
633C23—2442no—
634C23—2441no—
635C23—2441no—
636C23—2441no—
637C23—2441no—
638C23—2442no—
639C23—2442no—
640C23—2442no—
641C23—2442no—
642C23#1451973414yes—
643C23C22×C4×D6111yescharacteristic
644C23C2×D4×D6111yescharacteristic
645C23C2×D4×D6111yescharacteristic
646C23#41×D6112yes—
647C23C2×#1175822212yes—
648C23#1451982212yes—
649C23#1451982212yes—
650C23#1451982211yescharacteristic
651C23#1451982311yescharacteristic
652C23#1451982411yescharacteristic
653C23#1451982511yescharacteristic
654D4—12232no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—24no—
658C2×C4—24no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—416no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—614no—
680C2×C4—614no—
681C2×C4—1222no—
682C2×C4—1222no—
683C2×C4—1222no—
684C2×C4—1222no—
685C2×C4—1224no—
686C2×C4—1224no—
687C2×C4—1222no—
688C2×C4—1222no—
689C2×C4—1222no—
690C2×C4—1222no—
691C2×C4—1222no—
692C2×C4—1222no—
693C2×C4—1222no—
694C2×C4—24416no—
695C2×C4—2442no—
696C2×C4—2442no—
697C2×C4—2442no—
698C2×C4—2442no—
699C2×C4—2442no—
700C2×C4—2442no—
701C2×C4—2442no—
702C2×C4—2442no—
703C2×C4—2442no—
704C2×C4—2442no—
705C2×C4—2442no—
706C2×C4—2442no—
707C2×C4—2442no—
708C2×C4—2442no—
709C2×C4—2442no—
710C2×C4—2442no—
711C2×C4C22⋊C4×D6114yes—
712C22—24no—
713C22—24no—
714C22—24no—
715C22—42no—
716C22—42no—
717C22—44no—
718C22—44no—
719C22—44no—
720C22—44no—
721C22—42no—
722C22—42no—
723C22—1224no—
724C22—1224no—
725C22—1224no—
726C22—2442no—
727C22—2444no—
728C22—2444no—
729C22—2444no—
730C22—2444no—
731C22—2442no—
732C22—2442no—
733C22—2442no—
734C22C2×C22⋊C4×D6111yescharacteristic
735C22#117×D6111yescharacteristic
736C22C2×#1451973411yescharacteristic
737C22#1684023511yescharacteristic
738C22#1684023511yescharacteristic
739C22#1684024211yescharacteristic
740C22#1684024311yescharacteristic
741C22#1684027112yes—
742C22#1684027112yes—
743C22#1684032712yes—
744C22#1684032712yes—
745C22#1684032811yescharacteristic
746C22#1684033511yescharacteristic
747C22#1684034111yescharacteristic
748C22#1684034211yescharacteristic
749C22#1684034412yes—
750C22#1684034512yes—
751C22#1684034812yes—
752C22#1684035012yes—
753C22#1684035412yes—
754C22#1684035512yes—
755C22#1684035812yes—
756C22#1684035912yes—
757C4—24no—
758C4—42no—
759C4—82no—
760C4—82no—
761C4—1224no—
762C4—1224no—
763C4—4882no—
764C4—4882no—
765C4—2442no—
766C2—44no—
767C2—2444no—
768C2#2144820011yescharacteristic
769C2#2144840011yescharacteristic
770C2#2144840811yescharacteristic
771C2#2144844611yescharacteristic
772C2#2144844811yescharacteristic
773C2#2144845311yescharacteristic
774C2#2144845411yescharacteristic
775C2#2145167512yes—
776C2#2145169112yes—
777C2#2145172012yes—
778C2#2145172212yes—
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×C22⋊#95C2
socle, cosocleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenterC22⋊#95D61
hypocenterC61#14345
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#16839629C2semidirect
3. C2×#16839626C2semidirect
4. #21444085C2semidirect
5. #21444063C2semidirect
6. #21444062C2semidirect
8. #21444042C2semidirect
9. #21444040C2semidirect
10. #21444040C2semidirect
11. C61×C22⋊#95C2semidirect
16. C2×C4×C22⋊D61C4semidirect
206. C4×Dic61C22⋊C4semidirect
387. C22⋊#95D61semidirect
429. C61#14345semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D612
C2×#168396292
C2×#168396262
#214440852
#214440632
#214440622
#214440582
#214440422
#214440402
C61×C22⋊#952
#1434561