Finite Group Databasebeta

← #29601996

Subgroups — #29601996

Order 15616.

2510 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#11758196C211yesmaximal, characteristic
2C2×#16839637C211yesmaximal, characteristic
3C2×#16839635C211yesmaximal, characteristic
4C2×#16839634C211yesmaximal, characteristic
5C2×#16839631C212yesmaximal, complemented
6C2×#16839620C211yesmaximal, characteristic
7C2×C22⋊C4×Dic61C211yesmaximal, characteristic
8#21444083C212yesmaximal, complemented
9#21444082C212yesmaximal, complemented
10#21444047C212yesmaximal, complemented
11C2×C61×#385C211yesmaximal, characteristic
12C24×Dic61C2211yescharacteristic
13C24×Dic61C2211yescharacteristic
14C22×C4⋊Dic61C2212yes—
15C22×#11758196—28no—
16C22×#11758196—24no—
17C22×#11758196C2211yescharacteristic
18C22×#11758196C2212yes—
19C22×#11758196C2211yescharacteristic
20C22×#11758196C2212yes—
21C22×#11758196C2212yes—
22C22×#11758196C2212yes—
23C22×C22⋊Dic61C2211yescharacteristic
24C22×C22⋊Dic61C2211yescharacteristic
25C22×C4×Dic61C2212yes—
26#16839637—24no—
27#16839635—24no—
28#16839634—24no—
29#16839631—28no—
30#16839620—24no—
31C22⋊C4×Dic61C418yescomplemented
32C2×#14519684C2212yes—
33C2×#14519684C2212yes—
34C2×#14519684C2212yes—
35C2×#14519684C2211yescharacteristic
36C2×#14519684C2211yescharacteristic
37C2×#14519684C2212yes—
38C24×C4×C61C2211yescharacteristic
39C22×C4⋊C4×C61C2212yes—
40C22×C22⋊C4×C61C2211yescharacteristic
41C22×C22⋊C4×C61C2211yescharacteristic
42C61×#385—24no—
43C2×#95×C61C2212yes—
44C23×Dic61—24no—
45C23×Dic61—24no—
46C23×Dic61—22no—
47C23×Dic61—24no—
48C23×Dic61—22no—
49C23×Dic61—22no—
50C23×Dic61—42no—
51C23×Dic61C2×C414yes—
52C23×Dic61D414yes—
53C23×Dic61Q814yes—
54C23×Dic61C2311yescharacteristic
55C23×Dic61C2311yescharacteristic
56C23×Dic61C2312yes—
57C23×Dic61C2312yes—
58C23×Dic61C2311yescharacteristic
59C23×Dic61C2311yescharacteristic
60C2×C4⋊Dic61—24no—
61C2×C4⋊Dic61—24no—
62C2×C4⋊Dic61—42no—
63C2×#11758196—232no—
64C2×#11758196—24no—
65C2×#11758196—24no—
66C2×#11758196—24no—
67C2×#11758196—24no—
68C2×#11758196—24no—
69C2×#11758196—24no—
70C2×#11758196—22no—
71C2×#11758196—22no—
72C2×#11758196—24no—
73C2×#11758196—24no—
74C2×#11758196—24no—
75C2×#11758196—24no—
76C2×#11758196—24no—
77C2×#11758196—42no—
78C2×#11758196—42no—
79C2×#11758196D418yes—
80C2×C22⋊Dic61—22no—
81C2×C22⋊Dic61—22no—
82C2×C22⋊Dic61—22no—
83C2×C22⋊Dic61C2×C414yes—
84C2×C22⋊Dic61D414yes—
85C2×C22⋊Dic61Q814yes—
86C2×C4×Dic61—24no—
87C2×C4×Dic61—24no—
88C2×C4×Dic61C2×C418yescomplemented
89#14519684—24no—
90#14519684—22no—
91#14519684—22no—
92#14519684—24no—
93#14519684—24no—
94#14519684C2×C418yescomplemented
95C25×C61C2311yescharacteristic
96C23×C4×C61—22no—
97C23×C4×C61—24no—
98C23×C4×C61—22no—
99C23×C4×C61—22no—
100C23×C4×C61—42no—
101C23×C4×C61C2311yescharacteristic
102C23×C4×C61C2311yescharacteristic
103C23×C4×C61C2312yes—
104C23×C4×C61C2312yes—
105C2×C4⋊C4×C61—24no—
106C2×C4⋊C4×C61—24no—
107C2×C4⋊C4×C61—42no—
108C2×C22⋊C4×C61—22no—
109C2×C22⋊C4×C61—22no—
110C2×C22⋊C4×C61—22no—
111C2×C22⋊C4×C61C2×C414yes—
112C2×C22⋊C4×C61D414yes—
113C2×C22⋊C4×C61Q814yes—
114#95×C61—24no—
115C24×C61—22no—
116C24×C61—22no—
117C24×C61—22no—
118C24×C61—22no—
119C24×C61C22×C412yes—
120C24×C61C2×D412yes—
121C24×C61C2×D412yes—
122C24×C61C2×D412yes—
123C24×C61C2×Q812yes—
124C24×C61C2×Q812yes—
125C24×C61C2×Q812yes—
126C24×C61C2411yescharacteristic
127C22×C4×C61—22no—
128C22×C4×C61—22no—
129C22×C4×C61—22no—
130C22×C4×C61—22no—
131C22×C4×C61—28no—
132C22×C4×C61—22no—
133C22×C4×C61—22no—
134C22×C4×C61—22no—
135C22×C4×C61—22no—
136C22×C4×C61—22no—
137C22×C4×C61—22no—
138C22×C4×C61—21no—
139C22×C4×C61—21no—
140C22×C4×C61—21no—
141C22×C4×C61—21no—
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—48no—
149C22×C4×C61—48no—
150C22×C4×C61—44no—
151C22×C4×C61—44no—
152C22×C4×C61C22×C414yes—
153C22×C4×C61C2×D414yes—
154C22×C4×C61C2×D414yes—
155C22×C4×C61C2×Q814yes—
156C22×Dic61—22no—
157C22×Dic61—22no—
158C22×Dic61—22no—
159C22×Dic61—22no—
160C22×Dic61—22no—
161C22×Dic61—22no—
162C22×Dic61—216no—
163C22×Dic61—28no—
164C22×Dic61—216no—
165C22×Dic61—28no—
166C22×Dic61—28no—
167C22×Dic61—22no—
168C22×Dic61—22no—
169C22×Dic61—22no—
170C22×Dic61—22no—
171C22×Dic61—22no—
172C22×Dic61—22no—
173C22×Dic61—21no—
174C22×Dic61—21no—
175C22×Dic61—21no—
176C22×Dic61—21no—
177C22×Dic61—21no—
178C22×Dic61—21no—
179C22×Dic61—22no—
180C22×Dic61—22no—
181C22×Dic61—22no—
182C22×Dic61—22no—
183C22×Dic61—48no—
184C22×Dic61—48no—
185C22×Dic61—44no—
186C22×Dic61—44no—
187C22×Dic61C4⋊C4116yescomplemented
188C22×Dic61C22×C412yes—
189C22×Dic61C22×C414yes—
190C22×Dic61C22×C412yes—
191C22×Dic61C2×D414yes—
192C22×Dic61C2×D412yes—
193C22×Dic61C2×D414yes—
194C22×Dic61C2×D412yes—
195C22×Dic61C2×D414yes—
196C22×Dic61C2×Q812yes—
197C22×Dic61C2×Q814yes—
198C22×Dic61C2×Q812yes—
199C22×Dic61#4114yes—
200C4⋊C4×C61—48no—
201C22⋊C4×C61—44no—
202C22⋊C4×C61C4⋊C4116yescomplemented
203C22⋊Dic61—44no—
204C22⋊Dic61C4⋊C4116yescomplemented
205C4⋊Dic61—48no—
206#11758196—216no—
207#11758196—216no—
208#11758196—48no—
209#11758196—48no—
210#11758196—44no—
211#11758196—44no—
212C4×Dic61—216no—
213C23×C61—24no—
214C23×C61—24no—
215C23×C61—22no—
216C23×C61—24no—
217C23×C61—22no—
218C23×C61—22no—
219C23×C61—22no—
220C23×C61—24no—
221C23×C61—24no—
222C23×C61—24no—
223C23×C61—24no—
224C23×C61—24no—
225C23×C61—24no—
226C23×C61—24no—
227C23×C61—24no—
228C23×C61—24no—
229C23×C61C2×C4⋊C414yes—
230C23×C61C2×C4⋊C414yes—
231C23×C61C2×C4⋊C414yes—
232C23×C61#12714yes—
233C23×C61C4⋊Q814yes—
234C23×C61C4⋊Q814yes—
235C23×C61C4⋊Q814yes—
236C23×C61C23×C411yescharacteristic
237C23×C61C22×D411yescharacteristic
238C23×C61C22×D411yescharacteristic
239C23×C61C22×D411yescharacteristic
240C23×C61C22×D412yes—
241C23×C61C22×Q811yescharacteristic
242C23×C61C22×Q811yescharacteristic
243C23×C61C22×Q811yescharacteristic
244C23×C61C2×#4112yes—
245C23×C61H(5,𝔽2)12yes—
246C23×C612−1+412yes—
247C2×C4×C61—24no—
248C2×C4×C61—24no—
249C2×C4×C61—24no—
250C2×C4×C61—24no—
251C2×C4×C61—24no—
252C2×C4×C61—24no—
253C2×C4×C61—24no—
254C2×C4×C61—24no—
255C2×C4×C61—24no—
256C2×C4×C61—416no—
257C2×C4×C61—42no—
258C2×C4×C61—42no—
259C2×C4×C61—42no—
260C2×C4×C61—42no—
261C2×C4×C61—41no—
262C2×C4×C61—41no—
263C2×C4×C61—41no—
264C2×C4×C61—41no—
265C2×C4×C61—41no—
266C2×C4×C61—41no—
267C2×C4×C61—42no—
268C2×C4×C61—42no—
269C2×C4×C61—42no—
270C2×C4×C61—42no—
271C2×C4×C61C2×C4⋊C418yescomplemented
272C2×Dic61—24no—
273C2×Dic61—24no—
274C2×Dic61—24no—
275C2×Dic61—22no—
276C2×Dic61—24no—
277C2×Dic61—22no—
278C2×Dic61—24no—
279C2×Dic61—24no—
280C2×Dic61—24no—
281C2×Dic61—24no—
282C2×Dic61—232no—
283C2×Dic61—24no—
284C2×Dic61—24no—
285C2×Dic61—24no—
286C2×Dic61—416no—
287C2×Dic61—42no—
288C2×Dic61—42no—
289C2×Dic61—42no—
290C2×Dic61—42no—
291C2×Dic61—41no—
292C2×Dic61—41no—
293C2×Dic61—41no—
294C2×Dic61—41no—
295C2×Dic61—41no—
296C2×Dic61—41no—
297C2×Dic61—42no—
298C2×Dic61—42no—
299C2×Dic61—42no—
300C2×Dic61—42no—
301C2×Dic61C2×C4⋊C414yes—
302C2×Dic61C2×C4⋊C414yes—
303C2×Dic61C2×C4⋊C418yescomplemented
304C2×Dic61C4×D418yes—
305C2×Dic61#12014yes—
306C2×Dic61C22⋊Q818yes—
307C2×Dic61#12314yes—
308#13880—611nomaximal, Sylow
309C22×C61—24no—
310C22×C61—28no—
311C22×C61—28no—
312C22×C61—24no—
313C22×C61—24no—
314C22×C61—28no—
315C22×C61—28no—
316C22×C61—24no—
317C22×C61—24no—
318C22×C61—24no—
319C22×C61#38418yescomplemented
320C22×C61C22×C4⋊C411yescharacteristic
321C22×C61C22×C4⋊C411yescharacteristic
322C22×C61C22×C4⋊C411yescharacteristic
323C22×C61C2×C4×D412yes—
324C22×C61#52012yes—
325C22×C61C2×#12011yescharacteristic
326C22×C61C2×C22⋊Q812yes—
327C22×C61C2×#12311yescharacteristic
328C22×C61C2×#12711yescharacteristic
329C22×C61C2×C4⋊Q811yescharacteristic
330C22×C61C2×C4⋊Q811yescharacteristic
331C22×C61C2×C4⋊Q811yescharacteristic
332C22×C61#53511yescharacteristic
333C22×C61#53611yescharacteristic
334C22×C61#54412yes—
335C22×C61D4212yes—
336C22×C61D4212yes—
337C22×C61#54712yes—
338C22×C61#54712yes—
339C22×C61D4×Q812yes—
340C22×C61D4×Q812yes—
341C22×C61#55412yes—
342C22×C61#55412yes—
343C4×C61—28no—
344C4×C61—44no—
345C4×C61—81no—
346C4×C61—81no—
347Dic61—28no—
348Dic61—24no—
349Dic61—44no—
350Dic61—81no—
351Dic61—81no—
352Dic61#38518yescomplemented
353C23×C4⋊C4—611no—
354C2×#385—611no—
355C2×#385—611no—
356C2×#385—611no—
357C2×#385D6111yescharacteristic
358C2×#384—612no—
359C2×#380—611no—
360C2×C4×C22⋊C4—611no—
361#1444—612no—
362#1444—612no—
363C4⋊#95—612no—
364C2×C61—28no—
365C2×C61C2×#38411yescharacteristic
366C2×C61C2×#38511yescharacteristic
367C2×C61#231711yescharacteristic
368C2×C61D4×C4⋊C412yes—
369C2×C61D4×C4⋊C412yes—
370C2×C61#243311yescharacteristic
371C2×C61#243411yescharacteristic
372C2×C61#244012yes—
373C2×C61#244012yes—
374C2×C61#250111yescharacteristic
375C2×C61#250211yescharacteristic
376C24×C4—611no—
377C24×C4—611no—
378C24×C4C2×D6111yescharacteristic
379C22×C4⋊C4—612no—
380C22×C4⋊C4—612no—
381C22×C4⋊C4—611no—
382C22×C4⋊C4—611no—
383C22×C4⋊C4—612no—
384C22×C4⋊C4—612no—
385C22×C4⋊C4—612no—
386C22×C4⋊C4—1228no—
387C22×C4⋊C4—1224no—
388C22×C4⋊C4C2×D6112yes—
389C22×C22⋊C4—611no—
390C22×C22⋊C4—611no—
391C22×C22⋊C4C2×D6111yescharacteristic
392C22×C22⋊C4C2×D6111yescharacteristic
393C22×C42—612no—
394#385—24no—
395#385—1224no—
396#385—1224no—
397#385—1224no—
398#384—1228no—
399#380—1224no—
400C4×C22⋊C4—618no—
401C2×#95—612no—
402C2×#95—612no—
403C2×#95—612no—
404C2×#95—612no—
405C2×#95—611no—
406C2×#95—611no—
407C2×#95C2×D6112yes—
408C61#1388011yescharacteristic, complemented, Sylow
409C25C22×D6111yescharacteristic
410C23×C4—22no—
411C23×C4—24no—
412C23×C4—22no—
413C23×C4—22no—
414C23×C4—42no—
415C23×C4—611no—
416C23×C4—614no—
417C23×C4—614no—
418C23×C4—614no—
419C23×C4—612no—
420C23×C4—611no—
421C23×C4—612no—
422C23×C4—611no—
423C23×C4—611no—
424C23×C4—1224no—
425C23×C4—1224no—
426C23×C4—1224no—
427C23×C4—1222no—
428C23×C4—1222no—
429C23×C4—1222no—
430C23×C4—2442no—
431C23×C4C22×D6111yescharacteristic
432C23×C4C22×D6111yescharacteristic
433C23×C4C22×D6112yes—
434C23×C4C22×D6112yes—
435C2×C4⋊C4—24no—
436C2×C4⋊C4—24no—
437C2×C4⋊C4—42no—
438C2×C4⋊C4—618no—
439C2×C4⋊C4—1224no—
440C2×C4⋊C4—1224no—
441C2×C4⋊C4—1224no—
442C2×C4⋊C4—1224no—
443C2×C4⋊C4—12232no—
444C2×C4⋊C4—1224no—
445C2×C4⋊C4—1222no—
446C2×C4⋊C4—1222no—
447C2×C4⋊C4—1224no—
448C2×C4⋊C4—1224no—
449C2×C4⋊C4—1224no—
450C2×C4⋊C4—1224no—
451C2×C4⋊C4—1224no—
452C2×C4⋊C4—1224no—
453C2×C4⋊C4—1224no—
454C2×C4⋊C4—1224no—
455C2×C4⋊C4—2442no—
456C2×C4⋊C4—2442no—
457C2×C4⋊C4—2442no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—614no—
462C2×C22⋊C4—614no—
463C2×C22⋊C4—614no—
464C2×C22⋊C4—1222no—
465C2×C22⋊C4—1222no—
466C2×C22⋊C4—1222no—
467C2×C22⋊C4Dic12214yes—
468C2×C22⋊C4C4×D6114yes—
469C2×C22⋊C4C22⋊D6114yes—
470C2×C42—618no—
471C2×C42—1224no—
472C2×C42—1224no—
473#95—24no—
474#95—618no—
475#95—1222no—
476#95—1222no—
477#95—1224no—
478#95—1224no—
479#95—1224no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24C2×Dic12212yes—
485C24C2×C4×D6112yes—
486C24D4×D6112yes—
487C24D4×D6112yes—
488C24Q8×D6112yes—
489C24Q8×D6112yes—
490C24C2×C22⋊D6112yes—
491C24C23×D6111yescharacteristic
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—28no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—48no—
514C22×C4—48no—
515C22×C4—44no—
516C22×C4—44no—
517C22×C4—612no—
518C22×C4—614no—
519C22×C4—612no—
520C22×C4—612no—
521C22×C4—614no—
522C22×C4—612no—
523C22×C4—614no—
524C22×C4—614no—
525C22×C4—612no—
526C22×C4—614no—
527C22×C4—612no—
528C22×C4—6116no—
529C22×C4—614no—
530C22×C4—1228no—
531C22×C4—12216no—
532C22×C4—12216no—
533C22×C4—1228no—
534C22×C4—1222no—
535C22×C4—1222no—
536C22×C4—1222no—
537C22×C4—1222no—
538C22×C4—1222no—
539C22×C4—1222no—
540C22×C4—1228no—
541C22×C4—1222no—
542C22×C4—1222no—
543C22×C4—1222no—
544C22×C4—1222no—
545C22×C4—1222no—
546C22×C4—1222no—
547C22×C4—1221no—
548C22×C4—1221no—
549C22×C4—1221no—
550C22×C4—1221no—
551C22×C4—1222no—
552C22×C4—1221no—
553C22×C4—1221no—
554C22×C4—1222no—
555C22×C4—1222no—
556C22×C4—1222no—
557C22×C4—2448no—
558C22×C4—2448no—
559C22×C4—2444no—
560C22×C4—2444no—
561C22×C4C2×Dic12214yes—
562C22×C4C2×C4×D6114yes—
563C22×C4D4×D6114yes—
564C22×C4C2×C22⋊D6114yes—
565C4⋊C4—48no—
566C4⋊C4—12216no—
567C4⋊C4—12216no—
568C4⋊C4—2448no—
569C4⋊C4—2448no—
570C4⋊C4—2444no—
571C4⋊C4—2444no—
572C4⋊C4—2448no—
573C22⋊C4—44no—
574C22⋊C4—6116no—
575C22⋊C4—2444no—
576C22⋊C4#11758196116yescomplemented
577C42—12216no—
578C23—24no—
579C23—24no—
580C23—24no—
581C23—24no—
582C23—22no—
583C23—24no—
584C23—22no—
585C23—22no—
586C23—22no—
587C23—24no—
588C23—24no—
589C23—24no—
590C23—24no—
591C23—24no—
592C23—24no—
593C23—24no—
594C23C4⋊C4×D6114yes—
595C23C4⋊C4×D6114yes—
596C23C2×#1175819614yes—
597C23#1451977314yes—
598C23#1451977514yes—
599C23#1451977614yes—
600C23#1451977614yes—
601C23C22×C4×D6111yescharacteristic
602C23C2×D4×D6111yescharacteristic
603C23C2×D4×D6111yescharacteristic
604C23C2×D4×D6112yes—
605C23C22×C22⋊D6111yescharacteristic
606C23C2×Q8×D6111yescharacteristic
607C23C2×Q8×D6111yescharacteristic
608C23C22×Dic12211yescharacteristic
609C23#41×D6112yes—
610C23#1451982212yes—
611C23#1451982412yes—
612C2×C4—24no—
613C2×C4—24no—
614C2×C4—24no—
615C2×C4—24no—
616C2×C4—24no—
617C2×C4—24no—
618C2×C4—24no—
619C2×C4—24no—
620C2×C4—24no—
621C2×C4—416no—
622C2×C4—42no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—614no—
637C2×C4—618no—
638C2×C4—614no—
639C2×C4—618no—
640C2×C4—614no—
641C2×C4—614no—
642C2×C4—618no—
643C2×C4—12232no—
644C2×C4—1224no—
645C2×C4—1224no—
646C2×C4—1224no—
647C2×C4—1224no—
648C2×C4—1222no—
649C2×C4—1224no—
650C2×C4—1222no—
651C2×C4—1224no—
652C2×C4—1224no—
653C2×C4—1224no—
654C2×C4—1224no—
655C2×C4—1224no—
656C2×C4—1224no—
657C2×C4—2441no—
658C2×C4—2441no—
659C2×C4—2441no—
660C2×C4—2441no—
661C2×C4—2441no—
662C2×C4—2441no—
663C2×C4—2442no—
664C2×C4—2442no—
665C2×C4—2442no—
666C2×C4—2442no—
667C2×C4—24416no—
668C2×C4—2442no—
669C2×C4—2442no—
670C2×C4—2442no—
671C2×C4—2442no—
672C2×C4C2×#1175819618yescomplemented
673C22—28no—
674C22—28no—
675C22—24no—
676C22—28no—
677C22—28no—
678C22—24no—
679C22—24no—
680C22—24no—
681C22—24no—
682C22—24no—
683C22#1683963118yescomplemented
684C22C2×C4⋊C4×D6111yescharacteristic
685C22C2×C4⋊C4×D6111yescharacteristic
686C22C22×#1175819611yescharacteristic
687C22C4×D4×D6112yes—
688C22#1684024112yes—
689C22#120×D6111yescharacteristic
690C22C22⋊Q8×D6112yes—
691C22#123×D6111yescharacteristic
692C22C2×#1451977311yescharacteristic
693C22C2×#1451977511yescharacteristic
694C22C2×#1451977611yescharacteristic
695C22C2×#1451977611yescharacteristic
696C22#1684032711yescharacteristic
697C22#1684033411yescharacteristic
698C22#1684039112yes—
699C22#1684039412yes—
700C22D4×C22⋊D6112yes—
701C22#1684041012yes—
702C22#1684041112yes—
703C22#1684042512yes—
704C22D4×Dic12212yes—
705C22#1684046612yes—
706C22#1684047112yes—
707C4—28no—
708C4—44no—
709C4—81no—
710C4—81no—
711C4—618no—
712C4—1228no—
713C4—1224no—
714C4—4881no—
715C4—4881no—
716C4—2444no—
717C2—28no—
718C2C2×#1683963111yescharacteristic
719C2#385×D6111yescharacteristic
720C2#2144843811yescharacteristic
721C2D4×#1175819612yes—
722C2#2144871712yes—
723C2#2144945411yescharacteristic
724C2#2144946111yescharacteristic
725C2#2144951812yes—
726C2#2144952012yes—
727C2#2145028811yescharacteristic
728C2#2145029511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C61×#385C2
socle, cosocleC24×C61C24
prime radicalC25×C61C23
hypercenterC2×#385D61
hypocenterC61#13880
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
5. C2×#16839631C2semidirect
8. #21444083C2semidirect
9. #21444082C2semidirect
10. #21444047C2semidirect
31. C22⋊C4×Dic61C4semidirect
88. C2×C4×Dic61C2×C4semidirect
94. #14519684C2×C4semidirect
187. C22×Dic61C4⋊C4semidirect
202. C22⋊C4×C61C4⋊C4semidirect
204. C22⋊Dic61C4⋊C4semidirect
271. C2×C4×C61C2×C4⋊C4semidirect
303. C2×Dic61C2×C4⋊C4semidirect
319. C22×C61#384semidirect
352. Dic61#385semidirect
408. C61#13880semidirect
576. C22⋊C4#11758196semidirect
672. C2×C4C2×#11758196semidirect
683. C22#16839631semidirect

Maximal subgroups

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

subgroupindex
C23×#117581962
C2×#168396372
C2×#168396352
C2×#168396342
C2×#168396312
C2×#168396202
C2×C22⋊C4×Dic612
#214440832
#214440822
#214440472
C2×C61×#3852
#1388061