Finite Group Databasebeta

← #29608161

Subgroups — #29608161

Order 15616.

2386 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839665C212yesmaximal, complemented
2C2×#16839648C212yesmaximal, complemented
3#21444064C212yesmaximal, complemented
4#21444060C212yesmaximal, complemented
5#21444060C212yesmaximal, complemented
6#21444056C212yesmaximal, complemented
7#21444042C211yesmaximal, characteristic, complemented
8#21444042C211yesmaximal, characteristic, complemented
9C22×#121×C61C211yesmaximal, characteristic
10C22×C4⋊Dic61C2212yes—
11C22×C22⋊Dic61C2212yes—
12C22×C22⋊Dic61C2212yes—
13C22×C22⋊Dic61C2212yes—
14C22×C22⋊Dic61C2211yescharacteristic
15C22×C22⋊Dic61C2212yes—
16C22×C22⋊Dic61C2212yes—
17C22×C22⋊Dic61C2211yescharacteristic
18C22×C4×Dic61C2212yes—
19#16839665—28no—
20#16839648—28no—
21C2×#14519684C2212yes—
22C2×#14519684C2212yes—
23C2×#14519684C2212yes—
24C2×#14519684C2212yes—
25C2×#14519684C2211yescharacteristic
26C2×#14519684C2212yes—
27C2×#14519684C2211yescharacteristic
28C23×D4×C61C2212yes—
29C23×D4×C61C2211yescharacteristic
30C24×C4×C61C2211yescharacteristic
31C2×#121×C61—28no—
32C2×#121×C61C418yescomplemented
33C22×C4⋊C4×C61C2211yescharacteristic
34C22×C22⋊C4×C61C2212yes—
35C23×Dic61C2312yes—
36C23×Dic61C2312yes—
37C23×Dic61C2312yes—
38C23×Dic61C2312yes—
39C2×C4⋊Dic61—24no—
40C2×C4⋊Dic61—24no—
41C2×C4⋊Dic61—42no—
42C2×C22⋊Dic61—24no—
43C2×C22⋊Dic61—22no—
44C2×C22⋊Dic61—24no—
45C2×C22⋊Dic61—24no—
46C2×C22⋊Dic61—24no—
47C2×C22⋊Dic61—24no—
48C2×C22⋊Dic61—24no—
49C2×C22⋊Dic61—41no—
50C2×C22⋊Dic61—41no—
51C2×C22⋊Dic61—42no—
52C2×C22⋊Dic61—42no—
53C2×C22⋊Dic61—42no—
54C2×C22⋊Dic61—42no—
55C2×C22⋊Dic61—42no—
56C2×C22⋊Dic61—42no—
57C2×C22⋊Dic61—41no—
58C2×C22⋊Dic61—41no—
59C2×C22⋊Dic61—42no—
60C2×C22⋊Dic61—42no—
61C2×C22⋊Dic61—42no—
62C2×C22⋊Dic61D414yescomplemented
63C2×C4×Dic61—24no—
64C2×C4×Dic61—24no—
65C2×C4×Dic61—42no—
66#14519684—24no—
67#14519684—24no—
68#14519684—24no—
69#14519684—24no—
70#14519684—41no—
71#14519684—42no—
72#14519684—41no—
73C25×C61C2312yes—
74C25×C61C2311yescharacteristic
75C22×D4×C61—24no—
76C22×D4×C61—24no—
77C22×D4×C61—24no—
78C22×D4×C61—24no—
79C22×D4×C61—24no—
80C22×D4×C61—41no—
81C22×D4×C61—41no—
82C22×D4×C61—42no—
83C22×D4×C61—42no—
84C22×D4×C61—42no—
85C22×D4×C61C2×C418yes—
86C22×D4×C61C2×C414yes—
87C23×C4×C61—24no—
88C23×C4×C61—41no—
89C23×C4×C61—41no—
90C23×C4×C61—42no—
91C23×C4×C61C2×C414yes—
92C23×C4×C61C2311yescharacteristic
93C23×C4×C61C2312yes—
94C23×C4×C61C2311yescharacteristic
95#121×C61—232no—
96C2×C4⋊C4×C61C2×C414yes—
97C2×C4⋊C4×C61D418yes—
98C2×C22⋊C4×C61—24no—
99C2×C22⋊C4×C61—24no—
100C2×C22⋊C4×C61C2×C418yes—
101C24×C61—22no—
102C24×C61—22no—
103C24×C61—21no—
104C24×C61—21no—
105C24×C61—22no—
106C24×C61—22no—
107C24×C61—21no—
108C24×C61—21no—
109C24×C61—22no—
110C24×C61—22no—
111C24×C61—22no—
112C24×C61—22no—
113C24×C61—22no—
114C24×C61—22no—
115C24×C61—22no—
116C24×C61—22no—
117C24×C61—22no—
118C24×C61—22no—
119C24×C61—22no—
120C24×C61—22no—
121C24×C61—22no—
122C24×C61—22no—
123C24×C61C22×C414yes—
124C24×C61C22×C412yes—
125C24×C61C2×D412yes—
126C24×C61#4112yes—
127C24×C61C2411yescharacteristic
128C2×D4×C61—216no—
129C2×D4×C61—216no—
130C2×D4×C61—28no—
131C2×D4×C61—44no—
132C2×D4×C61—44no—
133C2×D4×C61—48no—
134C2×D4×C61—48no—
135C2×D4×C61—48no—
136C2×D4×C61—48no—
137C2×D4×C61—48no—
138C2×D4×C61—48no—
139C2×D4×C61—48no—
140C22×C4×C61—22no—
141C22×C4×C61—22no—
142C22×C4×C61—21no—
143C22×C4×C61—21no—
144C22×C4×C61—22no—
145C22×C4×C61—22no—
146C22×C4×C61—22no—
147C22×C4×C61—22no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—22no—
151C22×C4×C61—28no—
152C22×C4×C61—44no—
153C22×C4×C61—44no—
154C22×C4×C61—48no—
155C22×C4×C61—48no—
156C22×C4×C61C22×C412yes—
157C22×C4×C61C22×C414yes—
158C22×C4×C61C22×C412yes—
159C22×C4×C61C2×D414yes—
160C22×C4×C61C2×D414yes—
161C22×C4×C61C2×D414yes—
162C22×Dic61—22no—
163C22×Dic61—22no—
164C22×Dic61—22no—
165C22×Dic61—22no—
166C22×Dic61—22no—
167C22×Dic61—22no—
168C22×Dic61—22no—
169C22×Dic61—22no—
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×Dic61—22no—
187C22×Dic61—22no—
188C22×Dic61C2×D414yes—
189C22×Dic61#4114yes—
190C4⋊C4×C61C22⋊C4116yescomplemented
191C22⋊C4×C61—216no—
192C22⋊Dic61—44no—
193C22⋊Dic61—48no—
194C22⋊Dic61—48no—
195C22⋊Dic61—48no—
196C22⋊Dic61—48no—
197C22⋊Dic61—44no—
198C22⋊Dic61—48no—
199C4⋊Dic61—48no—
200C4×Dic61—48no—
201C23×C61—22no—
202C23×C61—22no—
203C23×C61—22no—
204C23×C61—22no—
205C23×C61—22no—
206C23×C61—22no—
207C23×C61—22no—
208C23×C61—22no—
209C23×C61—22no—
210C23×C61—22no—
211C23×C61—24no—
212C23×C61—24no—
213C23×C61—24no—
214C23×C61—24no—
215C23×C61—24no—
216C23×C61—24no—
217C23×C61—24no—
218C23×C61—24no—
219C23×C61—24no—
220C23×C61—24no—
221C23×C61—24no—
222C23×C61—42no—
223C23×C61—42no—
224C23×C61—42no—
225C23×C61—42no—
226C23×C61—42no—
227C23×C61—42no—
228C23×C61—42no—
229C23×C61—42no—
230C23×C61—42no—
231C23×C61—42no—
232C23×C61—42no—
233C23×C61—42no—
234C23×C61—42no—
235C23×C61—42no—
236C23×C61—42no—
237C23×C61—42no—
238C23×C61—42no—
239C23×C61—42no—
240C23×C61—42no—
241C23×C61—42no—
242C23×C61—42no—
243C23×C61—42no—
244C23×C61—42no—
245C23×C61—42no—
246C23×C61—42no—
247C23×C61—42no—
248C23×C61—42no—
249C23×C61—42no—
250C23×C61—42no—
251C23×C61—42no—
252C23×C61—42no—
253C23×C61—42no—
254C23×C61—42no—
255C23×C61—42no—
256C23×C61—42no—
257C23×C61—42no—
258C23×C61C4×D414yes—
259C23×C61C23×C411yescharacteristic
260C23×C61C22×D412yes—
261C23×C61C22×D411yescharacteristic
262C23×C61C2×#4111yescharacteristic
263C23×C61C2×#4112yes—
264C23×C61H(5,𝔽2)11yescharacteristic
265C23×C61H(5,𝔽2)11yescharacteristic
266C23×C61H(5,𝔽2)12yes—
267C23×C61H(5,𝔽2)12yes—
268C23×C61H(5,𝔽2)11yescharacteristic
269C23×C612−1+411yescharacteristic
270D4×C61—432no—
271D4×C61—416no—
272C2×C4×C61—24no—
273C2×C4×C61—22no—
274C2×C4×C61—22no—
275C2×C4×C61—24no—
276C2×C4×C61—24no—
277C2×C4×C61—24no—
278C2×C4×C61—24no—
279C2×C4×C61—24no—
280C2×C4×C61—24no—
281C2×C4×C61—24no—
282C2×C4×C61—22no—
283C2×C4×C61—22no—
284C2×C4×C61—22no—
285C2×C4×C61—416no—
286C2×C4×C61—42no—
287C2×C4×C61—42no—
288C2×C4×C61C2×C22⋊C418yes—
289C2×C4×C61C2×C22⋊C414yes—
290C2×Dic61—24no—
291C2×Dic61—24no—
292C2×Dic61—24no—
293C2×Dic61—24no—
294C2×Dic61—24no—
295C2×Dic61—24no—
296C2×Dic61—42no—
297C2×Dic61—42no—
298C2×Dic61—42no—
299C2×Dic61—42no—
300C2×Dic61—42no—
301C2×Dic61—42no—
302C2×Dic61—42no—
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—
318#14418—611nomaximal, Sylow
319C22×C61—24no—
320C22×C61—24no—
321C22×C61—24no—
322C22×C61—42no—
323C22×C61—42no—
324C22×C61—42no—
325C22×C61—42no—
326C22×C61—44no—
327C22×C61—44no—
328C22×C61—44no—
329C22×C61—44no—
330C22×C61—44no—
331C22×C61—44no—
332C22×C61—44no—
333C22×C61—44no—
334C22×C61—44no—
335C22×C61—44no—
336C22×C61—44no—
337C22×C61—82no—
338C22×C61—82no—
339C22×C61—82no—
340C22×C61—82no—
341C22×C61—82no—
342C22×C61—82no—
343C22×C61—82no—
344C22×C61—82no—
345C22×C61C22×C22⋊C411yescharacteristic
346C22×C61C2×C4×D411yescharacteristic
347C22×C61C4×#4111yescharacteristic
348C22×C61#51811yescharacteristic
349C22×C61#51811yescharacteristic
350C22×C61#51811yescharacteristic
351C22×C61#52011yescharacteristic
352C22×C61#53411yescharacteristic
353C22×C61#53512yes—
354C22×C61#53512yes—
355C22×C61#53711yescharacteristic
356C22×C61#53812yes—
357C22×C61#53811yescharacteristic
358C22×C61#53911yescharacteristic
359C22×C61#54012yes—
360C22×C61D4212yes—
361C22×C61#54612yes—
362C22×C61#54612yes—
363C22×C61#54812yes—
364C22×C61#55012yes—
365C22×C61#55312yes—
366C22×C61#56012yes—
367C22×C61#56212yes—
368C4×C61—24no—
369C4×C61—28no—
370C4×C61—42no—
371Dic61—44no—
372Dic61—44no—
373Dic61—82no—
374Dic61—82no—
375C22×#121D6111yescharacteristic
376C2×#390—612no—
377C2×#387—612no—
378#1439—612no—
379#1438—612no—
380#1438—612no—
381#1437—612no—
382C22⋊#95—611no—
383C22⋊#95—611no—
384C2×C61—44no—
385C2×C61—84no—
386C2×C61#230911yescharacteristic
387C2×C61#232511yescharacteristic
388C2×C61#233311yescharacteristic
389C2×C61D4×C22⋊C411yescharacteristic
390C2×C61#234111yescharacteristic
391C2×C61#236411yescharacteristic
392C2×C61#237711yescharacteristic
393C2×C61#267312yes—
394C2×C61#267612yes—
395C2×C61#271112yes—
396C2×C61#271412yes—
397C23×D4C2×D6112yes—
398C23×D4C2×D6111yescharacteristic
399C24×C4C2×D6111yescharacteristic
400C2×#121—28no—
401C2×#121Dic6118yescomplemented
402C22×C4⋊C4—612no—
403C22×C4⋊C4C2×D6111yescharacteristic
404C22×C22⋊C4—611no—
405C22×C22⋊C4—612no—
406C22×C22⋊C4—612no—
407C22×C22⋊C4—611no—
408C22×C22⋊C4—612no—
409C22×C22⋊C4—612no—
410C22×C22⋊C4—612no—
411C22×C22⋊C4C2×D6112yes—
412C22×C42—612no—
413#390—1228no—
414#387—1228no—
415C2×#95—612no—
416C2×#95—612no—
417C2×#95—612no—
418C2×#95—612no—
419C2×#95—611no—
420C2×#95—612no—
421C2×#95—611no—
422C61#1441811yescharacteristic, complemented, Sylow
423C25C22×D6112yes—
424C25C22×D6111yescharacteristic
425C22×D4—24no—
426C22×D4—24no—
427C22×D4—24no—
428C22×D4—24no—
429C22×D4—24no—
430C22×D4—42no—
431C22×D4—42no—
432C22×D4—42no—
433C22×D4—41no—
434C22×D4—41no—
435C22×D4C2×Dic6118yes—
436C22×D4C2×Dic6114yes—
437C23×C4—24no—
438C23×C4—42no—
439C23×C4—41no—
440C23×C4—41no—
441C23×C4—612no—
442C23×C4—612no—
443C23×C4—612no—
444C23×C4—612no—
445C23×C4C2×Dic6114yes—
446C23×C4C22×D6111yescharacteristic
447C23×C4C22×D6112yes—
448C23×C4C22×D6111yescharacteristic
449#121—232no—
450C2×C4⋊C4—1224no—
451C2×C4⋊C4—1224no—
452C2×C4⋊C4—2442no—
453C2×C4⋊C4C2×Dic6114yes—
454C2×C4⋊C4C22⋊D6118yes—
455C2×C22⋊C4—24no—
456C2×C22⋊C4—24no—
457C2×C22⋊C4—614no—
458C2×C22⋊C4—1224no—
459C2×C22⋊C4—1224no—
460C2×C22⋊C4—1224no—
461C2×C22⋊C4—1224no—
462C2×C22⋊C4—1224no—
463C2×C22⋊C4—1224no—
464C2×C22⋊C4—1222no—
465C2×C22⋊C4—2441no—
466C2×C22⋊C4—2441no—
467C2×C22⋊C4—2442no—
468C2×C22⋊C4—2442no—
469C2×C22⋊C4—2442no—
470C2×C22⋊C4—2442no—
471C2×C22⋊C4—2442no—
472C2×C22⋊C4—2442no—
473C2×C22⋊C4—2441no—
474C2×C22⋊C4—2441no—
475C2×C22⋊C4—2442no—
476C2×C22⋊C4—2442no—
477C2×C22⋊C4—2442no—
478C2×C22⋊C4C2×Dic6118yes—
479C2×C42—1224no—
480C2×C42—1224no—
481C2×C42—2442no—
482#95—1224no—
483#95—1224no—
484#95—1224no—
485#95—1224no—
486#95—2441no—
487#95—2442no—
488#95—2441no—
489C24—22no—
490C24—22no—
491C24—22no—
492C24—21no—
493C24—21no—
494C24—22no—
495C24—21no—
496C24—21no—
497C24—22no—
498C24—22no—
499C24—22no—
500C24—22no—
501C24—22no—
502C24—22no—
503C24—22no—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24—22no—
509C24—22no—
510C24—22no—
511C24D4×D6112yes—
512C24#1175822412yes—
513C24C22×Dic6114yes—
514C24C22×Dic6112yes—
515C24C23×D6111yescharacteristic
516C2×D4—216no—
517C2×D4—216no—
518C2×D4—28no—
519C2×D4—44no—
520C2×D4—44no—
521C2×D4—48no—
522C2×D4—48no—
523C2×D4—48no—
524C2×D4—48no—
525C2×D4—48no—
526C2×D4—48no—
527C2×D4—48no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—28no—
540C22×C4—44no—
541C22×C4—44no—
542C22×C4—48no—
543C22×C4—48no—
544C22×C4—614no—
545C22×C4—614no—
546C22×C4—1222no—
547C22×C4—1222no—
548C22×C4—1222no—
549C22×C4—1222no—
550C22×C4—1222no—
551C22×C4—1222no—
552C22×C4—1222no—
553C22×C4—1222no—
554C22×C4—1222no—
555C22×C4—1222no—
556C22×C4—1222no—
557C22×C4—1222no—
558C22×C4—1222no—
559C22×C4—1222no—
560C22×C4—1222no—
561C22×C4—1222no—
562C22×C4—1222no—
563C22×C4—1222no—
564C22×C4—1222no—
565C22×C4—1222no—
566C22×C4—1222no—
567C22×C4—1222no—
568C22×C4—1222no—
569C22×C4—1222no—
570C22×C4—1222no—
571C22×C4—1222no—
572C22×C4C22×Dic6112yes—
573C22×C4C22×Dic6114yes—
574C22×C4C22×Dic6112yes—
575C22×C4C2×C22⋊D6114yes—
576C22×C4C2×C22⋊D6114yes—
577C22×C4C2×C22⋊D6114yes—
578C4⋊C4—2448no—
579C4⋊C4C22⋊Dic61116yescomplemented
580C22⋊C4—216no—
581C22⋊C4—2444no—
582C22⋊C4—2448no—
583C22⋊C4—2448no—
584C22⋊C4—2448no—
585C22⋊C4—2448no—
586C22⋊C4—2444no—
587C22⋊C4—2448no—
588C42—2448no—
589C23—24no—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—22no—
594C23—22no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—24no—
601C23—24no—
602C23—24no—
603C23—24no—
604C23—24no—
605C23—24no—
606C23—24no—
607C23—24no—
608C23—24no—
609C23—24no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23D4×Dic6114yes—
647C23C23×Dic6111yescharacteristic
648C23C2×D4×D6111yescharacteristic
649C23C22×C22⋊D6112yes—
650C23#41×D6112yes—
651C23C2×#1175822411yescharacteristic
652C23#1451982212yes—
653C23#1451982212yes—
654C23#1451982211yescharacteristic
655C23#1451982211yescharacteristic
656C23#1451982311yescharacteristic
657C23#1451982411yescharacteristic
658D4—432no—
659D4—416no—
660C2×C4—24no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—416no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—1224no—
677C2×C4—1224no—
678C2×C4—1224no—
679C2×C4—1224no—
680C2×C4—1224no—
681C2×C4—1224no—
682C2×C4—2442no—
683C2×C4—2442no—
684C2×C4—2442no—
685C2×C4—2442no—
686C2×C4—2442no—
687C2×C4—2442no—
688C2×C4—2442no—
689C2×C4—2442no—
690C2×C4—2442no—
691C2×C4—2442no—
692C2×C4—2442no—
693C2×C4—2442no—
694C2×C4—2442no—
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×C4C2×C22⋊Dic6118yes—
705C2×C4C2×C22⋊Dic6114yes—
706C22—24no—
707C22—24no—
708C22—24no—
709C22—42no—
710C22—44no—
711C22—44no—
712C22—44no—
713C22—44no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—44no—
718C22—44no—
719C22—44no—
720C22—44no—
721C22—44no—
722C22—44no—
723C22—44no—
724C22—82no—
725C22—82no—
726C22—82no—
727C22—82no—
728C22—82no—
729C22—82no—
730C22—82no—
731C22—82no—
732C22C22×C22⋊Dic6111yescharacteristic
733C22C2×D4×Dic6111yescharacteristic
734C22#41×Dic6111yescharacteristic
735C22#1684023711yescharacteristic
736C22#1684023711yescharacteristic
737C22#1684023711yescharacteristic
738C22#1684024511yescharacteristic
739C22#1684032011yescharacteristic
740C22#1684032912yes—
741C22#1684032912yes—
742C22#1684033911yescharacteristic
743C22#1684034412yes—
744C22#1684034911yescharacteristic
745C22#1684035711yescharacteristic
746C22#1684036212yes—
747C22D4×C22⋊D6112yes—
748C22#1684040112yes—
749C22#1684040612yes—
750C22#1684041912yes—
751C22#1684043112yes—
752C22#1684045512yes—
753C22#1684050012yes—
754C22#1684050712yes—
755C4—28no—
756C4—24no—
757C4—42no—
758C4—4882no—
759C4—4882no—
760C4—2444no—
761C4—2444no—
762C2—44no—
763C2—84no—
764C2#2144840111yescharacteristic
765C2#2144852411yescharacteristic
766C2#2144858611yescharacteristic
767C2D4×C22⋊Dic6111yescharacteristic
768C2#2144866011yescharacteristic
769C2#2144887111yescharacteristic
770C2#2144897611yescharacteristic
771C2#2145208012yes—
772C2#2145211412yes—
773C2#2145257012yes—
774C2#2145260912yes—
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
Fitting, prime radicalC22×#121×C61C2
socle, cosocleC24×C61C24
hypercenterC22×#121D61
hypocenterC61#14418
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C2×#16839665C2semidirect
2. C2×#16839648C2semidirect
3. #21444064C2semidirect
4. #21444060C2semidirect
5. #21444060C2semidirect
6. #21444056C2semidirect
7. #21444042C2semidirect
8. #21444042C2semidirect
32. C2×#121×C61C4semidirect
62. C2×C22⋊Dic61D4semidirect
190. C4⋊C4×C61C22⋊C4semidirect
401. C2×#121Dic61semidirect
422. C61#14418semidirect
579. C4⋊C4C22⋊Dic61semidirect

Maximal subgroups

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

subgroupindex
C2×#168396652
C2×#168396482
#214440642
#214440602
#214440562
#214440422
C22×#121×C612
#1441861