Finite Group Databasebeta

← #29602201

Subgroups — #29602201

Order 15616.

2690 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839642C212yesmaximal
2C2×#16839637C212yesmaximal, complemented
3C2×#16839622C211yesmaximal, characteristic, complemented
4C22×#14519684C211yesmaximal, characteristic, complemented
5#21444072C212yesmaximal, complemented
6#21444064C212yesmaximal, complemented
7#21444049C211yesmaximal, characteristic, complemented
8#21444046C211yesmaximal, characteristic, complemented
9#21444042C211yesmaximal, characteristic, complemented
10#21444042C211yesmaximal, characteristic, complemented
11C22×C4×D4×C61C211yesmaximal, characteristic
12C24×Dic61C2212yes—
13C22×C4⋊Dic61C2212yes—
14C22×C4⋊Dic61C2212yes—
15C22×C22⋊Dic61C2212yes—
16C22×C22⋊Dic61C2212yes—
17C22×C22⋊Dic61C2212yes—
18#16839642—28no—
19#16839637—28no—
20#16839622—24no—
21C2×#14519684—24no—
22C2×#14519684C2211yescharacteristic
23C2×#14519684C2212yes—
24C2×#14519684C2212yes—
25C2×#14519684C2212yes—
26C2×#14519684C2212yes—
27C2×#14519684C2211yescharacteristic
28C2×#14519684C2211yescharacteristic
29C2×#14519684C2212yes—
30C2×#14519684C2212yes—
31C2×#14519684C2211yescharacteristic
32C23×D4×C61C2211yescharacteristic
33C24×C4×C61C2211yescharacteristic
34C24×C4×C61C2211yescharacteristic
35C2×C4×D4×C61—28no—
36C2×C4×D4×C61C418yescomplemented
37C22×C4⋊C4×C61C2211yescharacteristic
38C22×C22⋊C4×C61C2211yescharacteristic
39C22×C22⋊C4×C61C2211yescharacteristic
40C22×C42×C61C2211yescharacteristic
41C23×Dic61—24no—
42C23×Dic61—24no—
43C23×Dic61—24no—
44C23×Dic61—24no—
45C23×Dic61—24no—
46C23×Dic61—42no—
47C23×Dic61—42no—
48C23×Dic61C2312yes—
49C23×Dic61C2312yes—
50C23×Dic61C2312yes—
51C23×Dic61C2312yes—
52C2×C4⋊Dic61—24no—
53C2×C4⋊Dic61—24no—
54C2×C4⋊Dic61—24no—
55C2×C4⋊Dic61—24no—
56C2×C4⋊Dic61—42no—
57C2×C4⋊Dic61—42no—
58C2×C22⋊Dic61—24no—
59C2×C22⋊Dic61—24no—
60C2×C22⋊Dic61—24no—
61C2×C22⋊Dic61—24no—
62C2×C22⋊Dic61—24no—
63C2×C22⋊Dic61—24no—
64C2×C22⋊Dic61—24no—
65C2×C22⋊Dic61—42no—
66C2×C22⋊Dic61—42no—
67#14519684—22no—
68#14519684—22no—
69#14519684—24no—
70#14519684—24no—
71#14519684—24no—
72#14519684—24no—
73#14519684—22no—
74#14519684—24no—
75#14519684—42no—
76#14519684D414yescomplemented
77C25×C61C2311yescharacteristic
78C25×C61C2311yescharacteristic
79C22×D4×C61—24no—
80C22×D4×C61—24no—
81C22×D4×C61C2×C414yes—
82C22×D4×C61D414yes—
83C22×D4×C61Q814yes—
84C23×C4×C61—24no—
85C23×C4×C61—22no—
86C23×C4×C61—22no—
87C23×C4×C61—24no—
88C23×C4×C61—22no—
89C23×C4×C61—22no—
90C23×C4×C61—42no—
91C23×C4×C61—42no—
92C23×C4×C61C2×C414yes—
93C23×C4×C61C2×C414yescomplemented
94C23×C4×C61C2311yescharacteristic
95C23×C4×C61C2311yescharacteristic
96C23×C4×C61C2311yescharacteristic
97C23×C4×C61C2311yescharacteristic
98C23×C4×C61C2311yescharacteristic
99C4×D4×C61—232no—
100C2×C4⋊C4×C61—24no—
101C2×C4⋊C4×C61C2×C414yescomplemented
102C2×C22⋊C4×C61—24no—
103C2×C22⋊C4×C61C2×C414yes—
104C2×C22⋊C4×C61C2×C414yescomplemented
105C2×C22⋊C4×C61D418yes—
106C2×C42×C61—24no—
107C2×C42×C61C2×C414yescomplemented
108C24×C61—21no—
109C24×C61—22no—
110C24×C61—21no—
111C24×C61—21no—
112C24×C61—22no—
113C24×C61—21no—
114C24×C61—22no—
115C24×C61—21no—
116C24×C61—21no—
117C24×C61—22no—
118C24×C61—22no—
119C24×C61—22no—
120C24×C61—21no—
121C24×C61—21no—
122C24×C61C22×C412yes—
123C24×C61C22×C412yes—
124C24×C61C2×D412yes—
125C24×C61C2×D414yes—
126C24×C61C2×D412yes—
127C24×C61C2×Q812yes—
128C24×C61C2×Q812yes—
129C24×C61#4114yes—
130C24×C61C2411yescharacteristic
131C2×D4×C61—28no—
132C2×D4×C61—28no—
133C2×D4×C61—216no—
134C2×D4×C61—216no—
135C2×D4×C61C4⋊C4116yescomplemented
136C22×C4×C61—22no—
137C22×C4×C61—22no—
138C22×C4×C61—21no—
139C22×C4×C61—21no—
140C22×C4×C61—22no—
141C22×C4×C61—22no—
142C22×C4×C61—22no—
143C22×C4×C61—22no—
144C22×C4×C61—21no—
145C22×C4×C61—21no—
146C22×C4×C61—28no—
147C22×C4×C61—22no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—22no—
151C22×C4×C61—28no—
152C22×C4×C61—28no—
153C22×C4×C61—28no—
154C22×C4×C61—44no—
155C22×C4×C61—44no—
156C22×C4×C61—48no—
157C22×C4×C61—48no—
158C22×C4×C61—48no—
159C22×C4×C61—48no—
160C22×C4×C61C22×C412yes—
161C22×C4×C61C22×C412yes—
162C22×C4×C61C22×C412yes—
163C22×C4×C61C22×C412yes—
164C22×C4×C61C22×C412yes—
165C22×C4×C61C2×D414yes—
166C22×C4×C61C2×D414yes—
167C22×C4×C61C2×D412yes—
168C22×C4×C61C2×D412yes—
169C22×C4×C61C2×Q812yes—
170C22×C4×C61#4112yes—
171C22×Dic61—216no—
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×Dic61—22no—
189C22×Dic61—22no—
190C22×Dic61—22no—
191C22×Dic61—22no—
192C22×Dic61—22no—
193C22×Dic61—22no—
194C22×Dic61—22no—
195C22×Dic61—22no—
196C22×Dic61—22no—
197C22×Dic61—22no—
198C22×Dic61—48no—
199C22×Dic61—48no—
200C22×Dic61—48no—
201C22×Dic61—48no—
202C22×Dic61—48no—
203C22×Dic61—48no—
204C22×Dic61C2×D414yes—
205C22×Dic61#4114yes—
206C4⋊C4×C61—28no—
207C22⋊C4×C61—28no—
208C22⋊C4×C61C22⋊C4116yescomplemented
209C42×C61—28no—
210C22⋊Dic61—48no—
211C22⋊Dic61—48no—
212C22⋊Dic61—48no—
213C4⋊Dic61—48no—
214C4⋊Dic61—48no—
215C23×C61—22no—
216C23×C61—22no—
217C23×C61—22no—
218C23×C61—22no—
219C23×C61—24no—
220C23×C61—24no—
221C23×C61—24no—
222C23×C61—24no—
223C23×C61—22no—
224C23×C61—24no—
225C23×C61—24no—
226C23×C61—24no—
227C23×C61—24no—
228C23×C61—24no—
229C23×C61—22no—
230C23×C61—22no—
231C23×C61—22no—
232C23×C61—24no—
233C23×C61—22no—
234C23×C61—22no—
235C23×C61—22no—
236C23×C61—22no—
237C23×C61—22no—
238C23×C61—22no—
239C23×C61—24no—
240C23×C61—24no—
241C23×C61—22no—
242C23×C61—24no—
243C23×C61—22no—
244C23×C61—22no—
245C23×C61—22no—
246C23×C61—24no—
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×C61C2×C22⋊C414yes—
256C23×C61C2×C4⋊C414yes—
257C23×C61C2×C4⋊C414yes—
258C23×C61#11714yes—
259C23×C61#12118yes—
260C23×C61C22⋊Q818yes—
261C23×C61C23×C411yescharacteristic
262C23×C61C22×D412yes—
263C23×C61C22×D411yescharacteristic
264C23×C61C22×D411yescharacteristic
265C23×C61C22×Q811yescharacteristic
266C23×C61C2×#4112yes—
267C23×C61C2×#4111yescharacteristic
268C23×C61C2×#4112yes—
269C23×C61H(5,𝔽2)12yes—
270C23×C61H(5,𝔽2)11yescharacteristic
271C23×C612−1+411yescharacteristic
272D4×C61—232no—
273C2×C4×C61—22no—
274C2×C4×C61—22no—
275C2×C4×C61—22no—
276C2×C4×C61—22no—
277C2×C4×C61—22no—
278C2×C4×C61—22no—
279C2×C4×C61—22no—
280C2×C4×C61—22no—
281C2×C4×C61—24no—
282C2×C4×C61—24no—
283C2×C4×C61—24no—
284C2×C4×C61—24no—
285C2×C4×C61—24no—
286C2×C4×C61—24no—
287C2×C4×C61—24no—
288C2×C4×C61—24no—
289C2×C4×C61—22no—
290C2×C4×C61—22no—
291C2×C4×C61—22no—
292C2×C4×C61—416no—
293C2×C4×C61—416no—
294C2×C4×C61—42no—
295C2×C4×C61—42no—
296C2×C4×C61C2×C22⋊C414yes—
297C2×C4×C61C2×C22⋊C414yes—
298C2×C4×C61C2×C4⋊C414yes—
299C2×C4×C61C4×D414yes—
300C2×Dic61—24no—
301C2×Dic61—24no—
302C2×Dic61—24no—
303C2×Dic61—24no—
304C2×Dic61—24no—
305C2×Dic61—24no—
306C2×Dic61—432no—
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×Dic61—42no—
320C2×Dic61—42no—
321C2×Dic61—42no—
322C2×Dic61—42no—
323C2×Dic61—42no—
324C2×Dic61—42no—
325C2×Dic61—42no—
326C2×Dic61—42no—
327C2×Dic61—42no—
328C2×Dic61—42no—
329#13899—611nomaximal, Sylow
330C22×C61—24no—
331C22×C61—24no—
332C22×C61—24no—
333C22×C61—24no—
334C22×C61—24no—
335C22×C61—28no—
336C22×C61—28no—
337C22×C61—28no—
338C22×C61—28no—
339C22×C61—24no—
340C22×C61—24no—
341C22×C61—24no—
342C22×C61—24no—
343C22×C61—42no—
344C22×C61—42no—
345C22×C61—42no—
346C22×C61—44no—
347C22×C61—44no—
348C22×C61—44no—
349C22×C61—44no—
350C22×C61—42no—
351C22×C61#38018yescomplemented
352C22×C61C22×C22⋊C411yescharacteristic
353C22×C61C22×C4⋊C411yescharacteristic
354C22×C61C2×#11711yescharacteristic
355C22×C61C2×C4×D411yescharacteristic
356C22×C61C4×#4111yescharacteristic
357C22×C61#51811yescharacteristic
358C22×C61#52011yescharacteristic
359C22×C61C2×#12112yes—
360C22×C61C2×C22⋊Q812yes—
361C22×C61#52512yes—
362C22×C61#52912yes—
363C22×C61#53812yes—
364C22×C61#53912yes—
365C22×C61D4212yes—
366C22×C61D4211yescharacteristic
367C22×C61#54612yes—
368C22×C61#54612yes—
369C22×C61#54612yes—
370C22×C61#54712yes—
371C22×C61#54711yescharacteristic
372C22×C61D4×Q811yescharacteristic
373C22×C61#55411yescharacteristic
374C22×C61#55412yes—
375C4×C61—24no—
376C4×C61—24no—
377C4×C61—24no—
378C4×C61—24no—
379C4×C61—42no—
380Dic61—44no—
381Dic61—44no—
382Dic61—82no—
383Dic61—82no—
384C22×C4×D4D6111yescharacteristic
385C2×#386—612no—
386C2×#385—612no—
387C2×#380—611no—
388C22×#95—611no—
389#1441—612no—
390#1439—612no—
391C4⋊#95—611no—
392#1434—611no—
393C22⋊#95—611no—
394C22⋊#95—611no—
395C2×C61—28no—
396C2×C61—44no—
397C2×C61C2×#38011yescharacteristic
398C2×C61#229011yescharacteristic
399C2×C61#231811yescharacteristic
400C2×C61D4×C22⋊C411yescharacteristic
401C2×C61#233911yescharacteristic
402C2×C61D4×C4⋊C411yescharacteristic
403C2×C61#234911yescharacteristic
404C2×C61#242412yes—
405C2×C61#242512yes—
406C2×C61#244912yes—
407C2×C61#245012yes—
408C23×D4C2×D6111yescharacteristic
409C24×C4—612no—
410C24×C4C2×D6111yescharacteristic
411C24×C4C2×D6111yescharacteristic
412C2×C4×D4—28no—
413C2×C4×D4Dic6118yescomplemented
414C22×C4⋊C4—612no—
415C22×C4⋊C4—612no—
416C22×C4⋊C4C2×D6111yescharacteristic
417C22×C22⋊C4—612no—
418C22×C22⋊C4—612no—
419C22×C22⋊C4—612no—
420C22×C22⋊C4C2×D6111yescharacteristic
421C22×C22⋊C4C2×D6111yescharacteristic
422C22×C42C2×D6111yescharacteristic
423#386—1228no—
424#385—1228no—
425#380—1224no—
426C2×#95—611no—
427C2×#95—611no—
428C2×#95—611no—
429C2×#95—611no—
430C2×#95—612no—
431C2×#95—612no—
432C2×#95—612no—
433C2×#95—612no—
434C2×#95—612no—
435C2×#95—612no—
436C2×#95—1224no—
437C61#1389911yescharacteristic, complemented, Sylow
438C25C22×D6111yescharacteristic
439C25C22×D6111yescharacteristic
440C22×D4—24no—
441C22×D4—24no—
442C22×D4Dic12214yes—
443C22×D4D24414yes—
444C22×D4C2×Dic6114yes—
445C23×C4—24no—
446C23×C4—22no—
447C23×C4—22no—
448C23×C4—22no—
449C23×C4—22no—
450C23×C4—24no—
451C23×C4—42no—
452C23×C4—42no—
453C23×C4—612no—
454C23×C4—612no—
455C23×C4—612no—
456C23×C4—612no—
457C23×C4—1224no—
458C23×C4—1224no—
459C23×C4—1224no—
460C23×C4—1224no—
461C23×C4—1224no—
462C23×C4—2442no—
463C23×C4—2442no—
464C23×C4C2×Dic6114yes—
465C23×C4C2×Dic6114yescomplemented
466C23×C4C22×D6111yescharacteristic
467C23×C4C22×D6111yescharacteristic
468C23×C4C22×D6111yescharacteristic
469C23×C4C22×D6111yescharacteristic
470C23×C4C22×D6111yescharacteristic
471C4×D4—232no—
472C2×C4⋊C4—24no—
473C2×C4⋊C4—1224no—
474C2×C4⋊C4—1224no—
475C2×C4⋊C4—1224no—
476C2×C4⋊C4—1224no—
477C2×C4⋊C4—2442no—
478C2×C4⋊C4—2442no—
479C2×C4⋊C4C2×Dic6114yescomplemented
480C2×C22⋊C4—24no—
481C2×C22⋊C4—1224no—
482C2×C22⋊C4—1224no—
483C2×C22⋊C4—1224no—
484C2×C22⋊C4—1224no—
485C2×C22⋊C4—1224no—
486C2×C22⋊C4—1224no—
487C2×C22⋊C4—1224no—
488C2×C22⋊C4—2442no—
489C2×C22⋊C4—2442no—
490C2×C22⋊C4C2×Dic6114yes—
491C2×C22⋊C4C2×Dic6114yescomplemented
492C2×C22⋊C4C22⋊D6118yes—
493C2×C42—24no—
494C2×C42C2×Dic6114yescomplemented
495#95—614no—
496#95—1224no—
497#95—1224no—
498#95—1224no—
499#95—1222no—
500#95—1222no—
501#95—1222no—
502#95—1224no—
503#95—1224no—
504#95—2442no—
505C24—21no—
506C24—22no—
507C24—21no—
508C24—22no—
509C24—21no—
510C24—21no—
511C24—21no—
512C24—22no—
513C24—22no—
514C24—21no—
515C24—22no—
516C24—22no—
517C24—21no—
518C24—21no—
519C24C2×Dic12212yes—
520C24C2×Dic12212yes—
521C24C2×D24412yes—
522C24C2×D24412yes—
523C24#1175822214yes—
524C24C22×Dic6112yes—
525C24C22×Dic6112yes—
526C24C2×C22⋊D6114yes—
527C24C23×D6111yescharacteristic
528C2×D4—28no—
529C2×D4—28no—
530C2×D4—216no—
531C2×D4—216no—
532C2×D4C4⋊Dic61116yescomplemented
533C22×C4—21no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—21no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—22no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—28no—
548C22×C4—28no—
549C22×C4—28no—
550C22×C4—28no—
551C22×C4—44no—
552C22×C4—44no—
553C22×C4—48no—
554C22×C4—48no—
555C22×C4—48no—
556C22×C4—48no—
557C22×C4—614no—
558C22×C4—614no—
559C22×C4—12216no—
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×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—1222no—
581C22×C4—1222no—
582C22×C4—1222no—
583C22×C4—1222no—
584C22×C4—1222no—
585C22×C4—1222no—
586C22×C4—2448no—
587C22×C4—2448no—
588C22×C4—2448no—
589C22×C4—2448no—
590C22×C4—2448no—
591C22×C4—2448no—
592C22×C4C2×Dic12212yes—
593C22×C4C2×D24412yes—
594C22×C4D4×D6112yes—
595C22×C4#1175822412yes—
596C22×C4C22×Dic6112yes—
597C22×C4C22×Dic6112yes—
598C22×C4C22×Dic6112yes—
599C22×C4C22×Dic6112yes—
600C22×C4C22×Dic6112yes—
601C22×C4C2×C22⋊D6114yes—
602C22×C4C2×C22⋊D6114yes—
603C4⋊C4—28no—
604C4⋊C4—2448no—
605C4⋊C4—2448no—
606C22⋊C4—28no—
607C22⋊C4—2448no—
608C22⋊C4—2448no—
609C22⋊C4—2448no—
610C22⋊C4C22⋊Dic61116yescomplemented
611C42—28no—
612C23—22no—
613C23—24no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—24no—
619C23—24no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—22no—
624C23—24no—
625C23—24no—
626C23—24no—
627C23—24no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—24no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—24no—
639C23—24no—
640C23—22no—
641C23—24no—
642C23—22no—
643C23—22no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23C2×C22⋊Dic6114yes—
653C23C2×C4⋊Dic6114yes—
654C23C2×C4⋊Dic6114yes—
655C23#1451973614yes—
656C23#1451975118yes—
657C23#1451975618yes—
658C23C23×Dic6111yescharacteristic
659C23C2×D4×D6111yescharacteristic
660C23C22×C22⋊D6112yes—
661C23C22×D24411yescharacteristic
662C23C22×Dic12211yescharacteristic
663C23#41×D6112yes—
664C23C2×#1175822411yescharacteristic
665C23C2×#1175822212yes—
666C23#1451982212yes—
667C23#1451982311yescharacteristic
668C23#1451982411yescharacteristic
669D4—232no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—416no—
690C2×C4—416no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—1224no—
694C2×C4—1224no—
695C2×C4—1224no—
696C2×C4—1224no—
697C2×C4—1224no—
698C2×C4—1224no—
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×C4—2442no—
712C2×C4—2442no—
713C2×C4—24432no—
714C2×C4—2442no—
715C2×C4—2442no—
716C2×C4—2442no—
717C2×C4—2442no—
718C2×C4—2442no—
719C2×C4—2442no—
720C2×C4—2442no—
721C2×C4—2442no—
722C2×C4C2×C22⋊Dic6114yes—
723C2×C4C2×C22⋊Dic6114yes—
724C2×C4C2×C4⋊Dic6114yes—
725C2×C4D4×Dic6114yes—
726C22—24no—
727C22—24no—
728C22—24no—
729C22—24no—
730C22—28no—
731C22—28no—
732C22—28no—
733C22—28no—
734C22—24no—
735C22—24no—
736C22—24no—
737C22—24no—
738C22—24no—
739C22—42no—
740C22—42no—
741C22—44no—
742C22—44no—
743C22—44no—
744C22—44no—
745C22—42no—
746C22—42no—
747C22#1683962218yescomplemented
748C22C22×C22⋊Dic6111yescharacteristic
749C22C22×C4⋊Dic6111yescharacteristic
750C22C2×#1451973611yescharacteristic
751C22C2×D4×Dic6111yescharacteristic
752C22#41×Dic6111yescharacteristic
753C22#1684023711yescharacteristic
754C22#1684024511yescharacteristic
755C22C2×#1451975112yes—
756C22C2×#1451975612yes—
757C22#1684027112yes—
758C22#1684029212yes—
759C22#1684034512yes—
760C22#1684035412yes—
761C22D4×C22⋊D6112yes—
762C22D4×D24411yescharacteristic
763C22#1684040012yes—
764C22#1684040612yes—
765C22#1684040712yes—
766C22#1684041112yes—
767C22#1684041611yescharacteristic
768C22D4×Dic12211yescharacteristic
769C22#1684046911yescharacteristic
770C22#1684047112yes—
771C4—24no—
772C4—24no—
773C4—24no—
774C4—24no—
775C4—42no—
776C4—4882no—
777C4—4882no—
778C4—2444no—
779C4—2444no—
780C2—28no—
781C2—44no—
782C2C2×#1683962211yescharacteristic
783C2#2144826411yescharacteristic
784C2#2144845211yescharacteristic
785C2D4×C22⋊Dic6111yescharacteristic
786C2#2144864911yescharacteristic
787C2D4×C4⋊Dic6111yescharacteristic
788C2#2144872911yescharacteristic
789C2#2144934912yes—
790C2#2144936412yes—
791C2#2144962212yes—
792C2#2144963712yes—
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC22×C4×D4×C61C2
socle, cosocleC24×C61C24
prime radicalC23×D4×C61C22
hypercenterC22×C4×D4D61
hypocenterC61#13899
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×#16839637C2semidirect
3. C2×#16839622C2semidirect
4. C22×#14519684C2semidirect
5. #21444072C2semidirect
6. #21444064C2semidirect
7. #21444049C2semidirect
8. #21444046C2semidirect
9. #21444042C2semidirect
10. #21444042C2semidirect
36. C2×C4×D4×C61C4semidirect
76. #14519684D4semidirect
93. C23×C4×C61C2×C4semidirect
101. C2×C4⋊C4×C61C2×C4semidirect
104. C2×C22⋊C4×C61C2×C4semidirect
107. C2×C42×C61C2×C4semidirect
135. C2×D4×C61C4⋊C4semidirect
208. C22⋊C4×C61C22⋊C4semidirect
351. C22×C61#380semidirect
413. C2×C4×D4Dic61semidirect
437. C61#13899semidirect
465. C23×C4C2×Dic61semidirect
479. C2×C4⋊C4C2×Dic61semidirect
491. C2×C22⋊C4C2×Dic61semidirect
494. C2×C42C2×Dic61semidirect
532. C2×D4C4⋊Dic61semidirect
610. C22⋊C4C22⋊Dic61semidirect
747. C22#16839622semidirect

Maximal subgroups

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

subgroupindex
C2×#168396422
C2×#168396372
C2×#168396222
C22×#145196842
#214440722
#214440642
#214440492
#214440462
#214440422
C22×C4×D4×C612
#1389961